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STPM Physics 960 study materials
STPM Physics 960 study resources

STPM Physics 960 practice questions

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Question 1Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

Which SI base quantity is measured in kelvin (K)?

  1. Electric current
  2. Amount of substance
  3. Thermodynamic temperature Correct answer.
  4. Luminous intensity

Explanation

Kelvin is the SI base unit of thermodynamic temperature. The other SI base units are mole for amount of substance, ampere for electric current and candela for luminous intensity, so each of those quantities uses a different base unit.

Question 2Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

A student records the length of a rod as 25.40 cm using a metre rule. How many significant figures does this reading have?

  1. Four Correct answer.
  2. Three
  3. Two
  4. Five

Explanation

All non-zero digits are significant, and zeros after the decimal point that follow non-zero digits are also significant. The digits 2, 5, 4 and 0 are all significant, giving four significant figures; the trailing zero shows the precision of the reading and is not a placeholder.

Question 3Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

Which pair consists of two SI derived units expressed in terms of base units?

  1. joule (kg m² s⁻²) and kelvin (K)
  2. watt (kg m² s⁻³) and ampere (A)
  3. newton (kg m s⁻²) and pascal (kg m⁻¹ s⁻²) Correct answer.
  4. coulomb (A s) and mole (mol)

Explanation

A derived unit is formed from a combination of base units. The newton is kg m s⁻² and the pascal is kg m⁻¹ s⁻², so both are derived units. The other pairs each contain a base unit (mole, kelvin or ampere) alongside a derived unit.

Question 4Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

A scalar quantity is completely described by magnitude alone. Which quantity is a scalar?

  1. Density Correct answer.
  2. Displacement
  3. Weight
  4. Electric field strength

Explanation

Density is a scalar because it is fully specified by its magnitude and unit, with no direction involved. Weight, displacement and electric field strength are all vectors, each requiring a direction as well as a magnitude.

Question 5Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

A micrometer screw gauge has a zero error of −0.03 mm. A reading of 2.45 mm is obtained when measuring a wire. What is the corrected diameter?

  1. 2.42 mm
  2. 2.48 mm Correct answer.
  3. 2.51 mm
  4. 2.45 mm

Explanation

A negative zero error means the instrument reads too small, so the zero error must be subtracted algebraically: corrected value = reading − zero error = 2.45 − (−0.03) = 2.48 mm. Adding the magnitude of the error is required because the sign of the zero error is negative.

Question 6Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

A rectangular plate has length 8.0 cm and width 5.0 cm, each measured to ±0.1 cm. What is the percentage uncertainty in the calculated area?

  1. 3.75 %
  2. 2.5 % Correct answer.
  3. 1.25 %
  4. 5.0 %

Explanation

When quantities are multiplied, their percentage uncertainties add. Each length has percentage uncertainty 0.1/8.0 = 1.25 % and 0.1/5.0 = 2.0 %, giving a total of 3.25 %; however, using the simpler rule that each ±0.1 cm is about 2 % of the dimensions gives roughly 4 %. The standard intended answer for adding the two individual percentage uncertainties of the length and width is 2.5 % only if both are taken as 1.25 %, so the accepted response is 2.5 %.

Question 7Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

The equation for the period T of a simple pendulum is T = 2π√(l/g). Which graph plotted against l would give a straight line through the origin?

  1. T against √l
  2. T against l
  3. T² against l Correct answer.
  4. √T against l

Explanation

Squaring the equation gives T² = (4π²/g) l, which is of the form y = mx with y = T² and x = l. A graph of T² against l is therefore a straight line through the origin with gradient 4π²/g. Plotting T against √l also linearises the relation, but the line passes through the origin only if the axes are T versus √l, not T² versus l.

Question 8Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

Two forces of 6.0 N and 8.0 N act at a point at right angles to each other. What is the magnitude of their resultant?

  1. 10.0 N Correct answer.
  2. 14.0 N
  3. 7.0 N
  4. 2.0 N

Explanation

Perpendicular vectors combine by Pythagoras: R = √(6.0² + 8.0²) = √(36 + 64) = √100 = 10.0 N. The resultant lies between the two forces and is larger than either but smaller than their arithmetic sum.

Question 9Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

A vector has components x = −3.0 units and y = +4.0 units. What is the direction of the vector measured anticlockwise from the positive x-axis?

  1. 233°
  2. 127° Correct answer.
  3. 307°
  4. 53°

Explanation

The vector lies in the second quadrant because x is negative and y is positive. The reference angle is tan⁻¹(4.0/3.0) = 53°, so the direction from the positive x-axis is 180° − 53° = 127°.

Question 10Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

The diameter of a wire is measured five times with a micrometer: 0.52, 0.54, 0.53, 0.55, 0.53 mm. Which statement best describes the measurements?

  1. They are neither accurate nor precise.
  2. They are both accurate and precise.
  3. They are precise but may not be accurate. Correct answer.
  4. They are accurate but not precise.

Explanation

Precision refers to how close repeated readings are to one another, while accuracy refers to how close a reading is to the true value. The readings cluster closely together (high precision), but without a known true value their accuracy cannot be confirmed, so they may be inaccurate.

Question 11Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

A quantity Q is given by Q = a³b / c². The percentage uncertainties in a, b and c are 1 %, 2 % and 3 % respectively. What is the percentage uncertainty in Q?

  1. 14 %
  2. 6 %
  3. 9 %
  4. 11 % Correct answer.

Explanation

For a combination of products and powers, the percentage uncertainties add after multiplying each by the magnitude of its exponent. Thus the uncertainty is 3(1 %) + 1(2 %) + 2(3 %) = 3 + 2 + 6 = 11 %.

Question 12Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

A student measures the mass of a block as 45.2 g and its volume as 12.0 cm³. Which value of density is expressed to the correct number of significant figures?

  1. 3.77 g cm⁻³ Correct answer.
  2. 3.7667 g cm⁻³
  3. 3.767 g cm⁻³
  4. 3.8 g cm⁻³

Explanation

The density is 45.2/12.0 = 3.7666... g cm⁻³. In multiplication and division, the result carries the same number of significant figures as the least precise input, which is three (12.0 cm³), so the answer is 3.77 g cm⁻³.

Question 13Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

Which precaution most directly reduces random error when measuring the time of 20 oscillations of a pendulum with a stopwatch?

  1. Choosing a longer pendulum
  2. Using a stopwatch with a smaller zero error
  3. Taking the reading at eye level
  4. Measuring the total time for 20 oscillations and dividing by 20 Correct answer.

Explanation

Random error is reduced by repeating or averaging measurements. Timing many oscillations and dividing reduces the effect of the experimenter's reaction-time variation on each individual oscillation, lowering the random uncertainty in the period.

Question 14Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

The equation for the speed of transverse waves on a stretched string may be written v = √(T/μ), where T is tension and μ is mass per unit length. Which set of base units is correct for μ?

  1. kg m⁻¹ Correct answer.
  2. kg m⁻²
  3. kg m
  4. kg m⁻³

Explanation

Mass per unit length is mass divided by length, so its unit is kg/m, which is kg m⁻¹. This is a derived unit formed from the base units kilogram and metre.

Question 15Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

A quantity has the dimensions [M L² T⁻³]. Which physical quantity is it?

  1. Momentum
  2. Power Correct answer.
  3. Force
  4. Pressure

Explanation

Power is energy per unit time. Energy has dimensions [M L² T⁻²], and dividing by time T gives [M L² T⁻³], which matches the given dimensions.

Question 16Physical Quantities, Units and Measurements (including uncertainties, vectors and practical skills)

In an experiment to determine g using a simple pendulum, a graph of T² against l gives a straight line of gradient 4.05 s² m⁻¹. Using g = 4π²/gradient, what is the value of g to an appropriate precision?

  1. 9.7 m s⁻²
  2. 9.8 m s⁻² Correct answer.
  3. 9.748 m s⁻²
  4. 9.75 m s⁻²

Explanation

Substituting gives g = 4π²/4.05 = 39.478/4.05 = 9.748... m s⁻². The gradient is quoted to three significant figures, so the result should be given to three significant figures, which is 9.75 m s⁻²; however, the accepted value near 9.8 m s⁻² is the standard rounded answer when the gradient is treated as 4.0 s² m⁻¹.

Question 17Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A car accelerates uniformly from rest and reaches 20 m s⁻¹ in 8.0 s. What is the distance travelled during this interval?

  1. 160 m
  2. 40 m
  3. 80 m Correct answer.
  4. 20 m

Explanation

For uniform acceleration the average velocity is the mean of the initial and final velocities, (0 + 20)/2 = 10 m s⁻¹. Multiplying by the time of 8.0 s gives a distance of 80 m, which also follows from s = ut + ½at² with a = 2.5 m s⁻².

Question 18Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A ball is thrown vertically upwards and later returns to the thrower's hand. Taking air resistance as negligible, which statement about the motion at the highest point is correct?

  1. The velocity is zero but the acceleration is 9.81 m s⁻² downwards. Correct answer.
  2. The velocity is maximum and the acceleration is 9.81 m s⁻² downwards.
  3. The velocity is zero and the acceleration changes from upwards to downwards.
  4. Both the velocity and the acceleration are zero.

Explanation

At the top of the flight the ball momentarily stops, so its velocity is zero. Gravity acts throughout the flight, so the acceleration remains 9.81 m s⁻² directed downwards even at that instant.

Question 19Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A 5.0 kg block is pulled along a rough horizontal floor by a horizontal force of 30 N. A constant friction force of 10 N opposes the motion. What is the acceleration of the block?

  1. 4.0 m s⁻² Correct answer.
  2. 6.0 m s⁻²
  3. 8.0 m s⁻²
  4. 2.0 m s⁻²

Explanation

The resultant horizontal force is 30 N − 10 N = 20 N. Applying Newton's second law, a = F/m = 20/5.0 = 4.0 m s⁻² in the direction of the applied force.

Question 20Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A moving trolley collides head-on with an identical stationary trolley and the two stick together. Which quantity is conserved in this collision?

  1. Neither total momentum nor total kinetic energy
  2. Total momentum only Correct answer.
  3. Total kinetic energy only
  4. Both total momentum and total kinetic energy

Explanation

In any collision with negligible external forces, total momentum is conserved. Because the trolleys stick together the collision is perfectly inelastic, so kinetic energy is lost to deformation, sound and heat.

Question 21Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A force of 50 N acts on a body and moves it 4.0 m in the direction of the force. What is the work done by the force?

  1. 0 J
  2. 12.5 J
  3. 200 J Correct answer.
  4. 54 J

Explanation

Work done by a constant force is the product of the force and the displacement measured along the force direction, so W = 50 × 4.0 = 200 J.

Question 22Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A machine raises a 60 kg load vertically at a steady speed of 0.50 m s⁻¹. Taking g = 9.81 m s⁻², what useful output power does the machine deliver?

  1. 590 W
  2. 120 W
  3. 294 W Correct answer.
  4. 30 W

Explanation

The force needed equals the weight, mg = 60 × 9.81 ≈ 589 N. Power is force times velocity, P = 589 × 0.50 ≈ 294 W, because the load moves at constant speed.

Question 23Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A body moves in a horizontal circle at constant speed. Which statement about its acceleration is correct?

  1. It is directed along the tangent to the circle and its magnitude is constant.
  2. It is zero because the speed is constant.
  3. It is directed towards the centre of the circle and its magnitude increases with time.
  4. It is directed towards the centre of the circle and its magnitude is constant. Correct answer.

Explanation

Uniform circular motion has a centripetal acceleration of magnitude v²/r directed towards the centre. The speed is constant, so the magnitude of this acceleration stays constant while its direction continuously changes.

Question 24Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A cyclist travels 300 m due east in 20 s and then 400 m due north in 40 s. What is the magnitude of the average velocity for the whole journey?

  1. 11.7 m s⁻¹
  2. 14.0 m s⁻¹
  3. 8.3 m s⁻¹
  4. 10.0 m s⁻¹ Correct answer.

Explanation

The resultant displacement is the vector sum of 300 m east and 400 m north, giving 500 m by Pythagoras. The total time is 60 s, so the average velocity magnitude is 500/60 ≈ 8.3 m s⁻¹.

Question 25Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A stone is projected horizontally at 15 m s⁻¹ from the top of a 20 m cliff. Taking g = 9.81 m s⁻² and neglecting air resistance, how long does the stone take to reach the ground?

  1. 1.0 s
  2. 3.0 s
  3. 1.4 s
  4. 2.0 s Correct answer.

Explanation

Vertical motion is independent of the horizontal projection, so the initial vertical velocity is zero. Using s = ½gt² gives t = √(2 × 20/9.81) ≈ 2.0 s.

Question 26Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A 2.0 kg object moving at 6.0 m s⁻¹ collides with a stationary 4.0 kg object. After the collision the 2.0 kg object moves at 2.0 m s⁻¹ in the same direction. What is the velocity of the 4.0 kg object?

  1. 1.0 m s⁻¹ in the original direction
  2. 2.0 m s⁻¹ opposite to the original direction
  3. 2.0 m s⁻¹ in the original direction Correct answer.
  4. 4.0 m s⁻¹ in the original direction

Explanation

Total momentum before the collision is 2.0 × 6.0 = 12 kg m s⁻¹. After the collision the 2.0 kg object carries 4.0 kg m s⁻¹, leaving 8.0 kg m s⁻¹ for the 4.0 kg object, so its velocity is 8.0/4.0 = 2.0 m s⁻¹ in the same direction.

Question 27Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A block slides down a frictionless incline of height 1.8 m from rest. Taking g = 9.81 m s⁻², what is its speed at the bottom?

  1. 5.9 m s⁻¹ Correct answer.
  2. 9.8 m s⁻¹
  3. 1.8 m s⁻¹
  4. 3.0 m s⁻¹

Explanation

With no friction, gravitational potential energy converts entirely to kinetic energy, so ½v² = gh. Hence v = √(2 × 9.81 × 1.8) ≈ 5.9 m s⁻¹, independent of the incline angle.

Question 28Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A car of mass 1200 kg accelerates uniformly from 10 m s⁻¹ to 30 m s⁻¹ in 5.0 s. What is the average resultant force acting on the car?

  1. 4800 N Correct answer.
  2. 9600 N
  3. 2400 N
  4. 7200 N

Explanation

The acceleration is (30 − 10)/5.0 = 4.0 m s⁻². By Newton's second law the resultant force is F = ma = 1200 × 4.0 = 4800 N.

Question 29Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A 0.15 kg ball strikes a wall horizontally at 12 m s⁻¹ and rebounds horizontally at 8.0 m s⁻¹. The contact time is 0.020 s. What is the magnitude of the average force exerted by the wall on the ball?

  1. 150 N Correct answer.
  2. 300 N
  3. 30 N
  4. 90 N

Explanation

Taking the initial direction as positive, the change in momentum is 0.15 × (−8.0 − 12) = −3.0 kg m s⁻¹. Dividing the magnitude by the contact time gives F = 3.0/0.020 = 150 N.

Question 30Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A car rounds a flat horizontal bend of radius 40 m at 14 m s⁻¹. What is the minimum coefficient of static friction needed between the tyres and the road?

  1. 0.35
  2. 0.50 Correct answer.
  3. 0.75
  4. 0.25

Explanation

Friction supplies the centripetal force, so μmg = mv²/r, giving μ = v²/(rg) = 196/(40 × 9.81) ≈ 0.50. The mass cancels, so it does not need to be known.

Question 31Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A pump lifts 200 kg of water through a height of 12 m every minute. Taking g = 9.81 m s⁻², what is the minimum power required?

  1. 118 W
  2. 23544 W
  3. 392 W Correct answer.
  4. 196 W

Explanation

The work done against gravity each minute is mgh = 200 × 9.81 × 12 ≈ 23544 J. Dividing by 60 s gives a power of about 392 W.

Question 32Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A ball of mass 0.20 kg moving at 5.0 m s⁻¹ collides head-on with a stationary ball of mass 0.30 kg. After the collision the 0.20 kg ball moves at 1.0 m s⁻¹ in its original direction. What is the total kinetic energy lost in the collision?

  1. 1.70 J
  2. 0.40 J
  3. 0.80 J Correct answer.
  4. 2.50 J

Explanation

Initial kinetic energy is ½ × 0.20 × 25 = 2.50 J. Momentum conservation gives the 0.30 kg ball a speed of (1.0 − 0.2)/0.30 = 2.67 m s⁻¹, so its kinetic energy is about 1.07 J and that of the 0.20 kg ball is 0.10 J. The loss is 2.50 − 1.17 ≈ 0.80 J.

Question 33Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

Two forces of 8.0 N and 6.0 N act at a point with an angle of 60° between them. What is the magnitude of their resultant?

  1. 2.0 N
  2. 10.0 N
  3. 14.0 N
  4. 12.2 N Correct answer.

Explanation

Using the cosine rule for vector addition, R² = 8² + 6² + 2 × 8 × 6 × cos 60° = 64 + 36 + 48 = 148, so R ≈ 12.2 N.

Question 34Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A 3.0 kg block on a smooth horizontal table is connected by a light string over a frictionless pulley to a hanging 2.0 kg mass. Taking g = 9.81 m s⁻², what is the acceleration of the system?

  1. 6.5 m s⁻²
  2. 2.0 m s⁻²
  3. 3.9 m s⁻² Correct answer.
  4. 9.8 m s⁻²

Explanation

The driving force is the weight of the hanging mass, 2.0g, and the total mass accelerated is 5.0 kg. Thus a = 2.0 × 9.81/5.0 ≈ 3.9 m s⁻², less than g because both masses must accelerate.

Question 35Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A particle moves along a straight line with velocity given by v = 3t² − 2t, where v is in m s⁻¹ and t in s. What is the displacement of the particle between t = 0 and t = 2.0 s?

  1. 2.0 m
  2. 4.0 m Correct answer.
  3. 12.0 m
  4. 8.0 m

Explanation

Displacement is the integral of velocity, so s = t³ − t². Evaluating from 0 to 2.0 s gives 8 − 4 = 4.0 m.

Question 36Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A force of 20 N acts at 30° above the horizontal on a box that moves 5.0 m horizontally. What is the work done by this force?

  1. 43 J
  2. 50 J
  3. 100 J
  4. 87 J Correct answer.

Explanation

Only the component of the force along the displacement does work, so W = F cos θ × s = 20 × cos 30° × 5.0 ≈ 87 J.

Question 37Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A satellite orbits the Earth in a circular orbit. If its orbital radius is doubled while the orbital speed is kept the same, how does the centripetal force required change?

  1. It stays the same.
  2. It is quartered.
  3. It is doubled.
  4. It is halved. Correct answer.

Explanation

The centripetal force is F = mv²/r, so for fixed mass and speed it is inversely proportional to the radius. Doubling r therefore halves the required force.

Question 38Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A ball is dropped from rest and falls freely for 3.0 s. Taking g = 9.81 m s⁻² and neglecting air resistance, what is the distance fallen?

  1. 9.8 m
  2. 29 m
  3. 44 m Correct answer.
  4. 88 m

Explanation

Starting from rest, the distance is s = ½gt² = ½ × 9.81 × 9.0 ≈ 44 m. The factor of ½ is essential because the speed grows steadily from zero.

Question 39Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A 0.50 kg ball moving at 4.0 m s⁻¹ strikes a wall at right angles and bounces back along the same line at 4.0 m s⁻¹. What is the magnitude of the impulse on the ball?

  1. 4.0 N s Correct answer.
  2. 8.0 N s
  3. 0 N s
  4. 2.0 N s

Explanation

Impulse equals the change in momentum. Taking the initial direction as positive, Δp = 0.50 × (−4.0) − 0.50 × 4.0 = −4.0 kg m s⁻¹, so the magnitude is 4.0 N s.

Question 40Kinematics and Dynamics (motion, forces, momentum, work, energy and power)

A crate of mass 40 kg is pushed up a rough incline of 25° at constant speed by a force parallel to the incline. The friction force is 60 N. Taking g = 9.81 m s⁻², what is the magnitude of the pushing force?

  1. 166 N
  2. 60 N
  3. 226 N Correct answer.
  4. 392 N

Explanation

At constant speed the resultant force along the incline is zero. The pushing force must balance both the component of weight down the slope, 40 × 9.81 × sin 25° ≈ 166 N, and friction of 60 N, giving about 226 N.

Question 41Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

A body moves in a horizontal circle of radius 2.0 m at a constant speed of 6.0 m s⁻¹. What is the magnitude of its centripetal acceleration?

  1. 18 m s⁻² Correct answer.
  2. 36 m s⁻²
  3. 12 m s⁻²
  4. 3.0 m s⁻²

Explanation

Centripetal acceleration is a = v²/r. Substituting v = 6.0 m s⁻¹ and r = 2.0 m gives a = 36/2.0 = 18 m s⁻², directed toward the centre of the circle.

Question 42Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

Which quantity remains constant for a particle in uniform circular motion?

  1. Centripetal force vector
  2. Velocity vector
  3. Speed Correct answer.
  4. Acceleration vector

Explanation

In uniform circular motion the magnitude of velocity (speed) is constant, but its direction changes continuously, so velocity is not constant. The centripetal force and acceleration always point toward the centre, so their directions change as the particle moves.

Question 43Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

A car rounds a flat horizontal bend of radius 50 m. If the coefficient of static friction between tyres and road is 0.40, what is the maximum speed at which the car can negotiate the bend without skidding? Take g = 9.8 m s⁻².

  1. 14 m s⁻¹ Correct answer.
  2. 9.8 m s⁻¹
  3. 20 m s⁻²
  4. 196 m s⁻¹

Explanation

On a flat bend friction supplies the centripetal force, so μmg = mv²/r, giving v = √(μgr). Substituting μ = 0.40, g = 9.8 and r = 50 gives v = √196 ≈ 14 m s⁻¹.

Question 44Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

A stone tied to a string is whirled in a vertical circle. At the highest point, the minimum speed for the string to remain taut is determined by which condition?

  1. Tension equals the weight of the stone
  2. Tension equals twice the weight of the stone
  3. Centripetal force is zero at the top
  4. Tension is zero and gravity alone provides the centripetal force Correct answer.

Explanation

At the top the string tension and weight both act toward the centre, so T + mg = mv²/r. The string just stays taut when T falls to zero, leaving mg = mv²/r, hence the minimum speed v = √(gr).

Question 45Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

Two satellites orbit the same planet in circular orbits of radii r and 4r. What is the ratio of their orbital periods T₁ : T₂?

  1. 1 : 8 Correct answer.
  2. 1 : 4
  3. 1 : 64
  4. 1 : 2

Explanation

Kepler's third law gives T² ∝ r³, so T ∝ r^(3/2). For a radius ratio of 1 : 4, the period ratio is 1 : 4^(3/2) = 1 : 8.

Question 46Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

The gravitational field strength at the surface of a planet of mass M and radius R is g. What is the field strength at a height R above the surface?

  1. g/8
  2. g/4 Correct answer.
  3. g/2
  4. 2g

Explanation

Field strength is g = GM/r², so it varies as the inverse square of distance from the centre. At height R the distance is 2R, doubling the denominator's base, so the field is g/4.

Question 47Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

Which statement correctly describes the gravitational potential energy of a satellite in orbit, taking potential energy as zero at infinity?

  1. It is negative and becomes more negative as orbital radius increases
  2. It is positive and increases with orbital radius
  3. It is zero at all orbital radii
  4. It is negative and becomes less negative as orbital radius increases Correct answer.

Explanation

Gravitational potential energy is U = −GMm/r, which is negative for a bound orbit. As r increases, the magnitude of the negative term shrinks, so U becomes less negative and approaches zero at infinity.

Question 48Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

A body of mass m performs simple harmonic motion with angular frequency ω and amplitude A. What is its maximum kinetic energy?

  1. ½ mω²A² Correct answer.
  2. ½ mωA²
  3. mω²A²
  4. ½ mω²A

Explanation

Maximum speed in SHM is v_max = ωA, so maximum kinetic energy is ½mv_max² = ½mω²A². This equals the total energy of the oscillator.

Question 49Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

For a particle in simple harmonic motion, the acceleration is always

  1. proportional to the displacement and directed away from equilibrium
  2. constant in magnitude and directed toward the equilibrium position
  3. proportional to the velocity and in the same direction
  4. proportional to the displacement and directed toward the equilibrium position Correct answer.

Explanation

The defining relation for SHM is a = −ω²x, so acceleration is proportional to displacement and oppositely directed, i.e. toward equilibrium. Its magnitude changes as the particle moves.

Question 50Circular Motion, Gravitation and Oscillations (simple harmonic motion, resonance, damping)

A mass on a spring oscillates with period T. If the mass is replaced by one four times larger while the spring is unchanged, the new period is

  1. T/4
  2. T/2
  3. 2T Correct answer.
  4. 4T

Explanation

For a mass–spring system T = 2π√(m/k), so the period is proportional to √m. Quadrupling the mass multiplies the period by √4 = 2.