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Question 1Mechanics
A car travels 120 m due east in 15 s and then 80 m due west in 10 s. What is the magnitude of its average velocity for the whole journey?
- 8.0 m/s
- 1.6 m/s Correct answer.
- 2.4 m/s
- 0.8 m/s
Explanation
Average velocity depends on total displacement, not total distance. The displacement is 120 − 80 = 40 m east, and the total time is 25 s, so the magnitude is 40/25 = 1.6 m/s.
Question 2Mechanics
Which statement correctly describes the acceleration of a body moving with uniform velocity?
- It is zero because the velocity does not change Correct answer.
- It is constant and non-zero
- It is equal to the velocity divided by time
- It increases steadily with time
Explanation
Acceleration is the rate of change of velocity. Uniform velocity means the velocity vector stays the same in both magnitude and direction, so its rate of change is zero and the acceleration is zero.
Question 3Mechanics
A stone is dropped from rest and falls freely for 3.0 s. Taking g = 10 m/s², how far does it fall?
- 45 m Correct answer.
- 90 m
- 30 m
- 15 m
Explanation
For free fall from rest, the distance is s = ½gt². Substituting gives s = ½ × 10 × 3.0² = 45 m.
Question 4Mechanics
A body moves in a straight line with constant acceleration. Its velocity–time graph is a straight line. What does the area under this graph represent?
- The average velocity of the body
- The acceleration of the body
- The displacement of the body Correct answer.
- The change in acceleration
Explanation
On a velocity–time graph, velocity multiplied by time interval gives displacement, which is exactly the area under the line. The gradient of the line, not the area, gives acceleration.
Question 5Mechanics
Two forces of 6 N and 8 N act at a point at right angles to each other. What is the magnitude of their resultant?
- 10 N Correct answer.
- 14 N
- 2 N
- 48 N
Explanation
For perpendicular forces the resultant is found from Pythagoras: R = √(6² + 8²) = √100 = 10 N.
Question 6Mechanics
A body of mass 5 kg is acted on by a net force of 20 N. What is its acceleration?
- 4 m/s² Correct answer.
- 0.25 m/s²
- 100 m/s²
- 25 m/s²
Explanation
Newton's second law states F = ma, so a = F/m. Substituting gives a = 20/5 = 4 m/s².
Question 7Mechanics
Which quantity is a measure of the inertia of a body?
- Its weight
- Its velocity
- Its mass Correct answer.
- Its momentum
Explanation
Inertia is the tendency of a body to resist changes in its state of motion, and mass is the quantitative measure of that inertia. Weight and momentum depend on other quantities such as gravity or velocity.
Question 8Mechanics
A force of 50 N acts on a spanner at a perpendicular distance of 0.20 m from the pivot. What is the moment of the force about the pivot?
- 0.004 N m
- 10 N m Correct answer.
- 2.5 N m
- 250 N m
Explanation
The moment of a force is the product of the force and the perpendicular distance from the pivot. Hence moment = 50 × 0.20 = 10 N m.
Question 9Mechanics
A block slides across a rough horizontal surface and gradually slows down. Which statement about the forces on the block is correct?
- Kinetic friction acts in the direction of motion
- Kinetic friction acts opposite to the motion and the net force is non-zero Correct answer.
- The net force on the block is zero while it slows down
- The normal reaction is greater than the weight of the block
Explanation
Kinetic friction always opposes relative sliding, so it points opposite to the velocity and produces a deceleration. Because the velocity is changing, the net force must be non-zero.
Question 10Mechanics
A body starts from rest and accelerates uniformly at 2 m/s² for 5 s. What distance does it cover in this time?
- 10 m
- 100 m
- 25 m Correct answer.
- 50 m
Explanation
Using s = ut + ½at² with u = 0 gives s = ½ × 2 × 5² = 25 m.
Question 11Mechanics
A ball is thrown vertically upwards with a speed of 20 m/s. Taking g = 10 m/s² and ignoring air resistance, what is the maximum height reached?
- 10 m
- 2 m
- 20 m Correct answer.
- 40 m
Explanation
At the highest point the velocity is zero, so using v² = u² − 2gs gives 0 = 20² − 2 × 10 × s, hence s = 400/20 = 20 m.
Question 12Mechanics
A body moves in a horizontal circle at constant speed. Which statement about its acceleration is correct?
- It is zero because the speed is constant
- It is directed along the tangent to the circle
- It is directed towards the centre and has magnitude v²/r Correct answer.
- It is directed away from the centre and equals v/r
Explanation
Although the speed is constant, the direction of velocity changes continuously, so there is a centripetal acceleration. This acceleration points towards the centre of the circle and has magnitude v²/r.
Question 13Mechanics
A satellite orbits a planet in a circular path. If the radius of the orbit is halved while the speed is unchanged, the centripetal force required becomes
- twice as large Correct answer.
- half as large
- four times as large
- unchanged
Explanation
The centripetal force is F = mv²/r, so for fixed mass and speed the force is inversely proportional to the radius. Halving r therefore doubles the required force.
Question 14Mechanics
A body of mass 2 kg moving at 6 m/s collides with a stationary body of mass 4 kg, and they stick together. What is their common velocity after the collision?
- 4 m/s
- 3 m/s
- 1 m/s
- 2 m/s Correct answer.
Explanation
Momentum is conserved in the collision. Initial momentum = 2 × 6 = 12 kg m/s, and total mass after sticking is 6 kg, so v = 12/6 = 2 m/s.
Question 15Mechanics
A force of 100 N acts on a body for 0.5 s. What impulse does it deliver?
- 200 N s
- 150 N s
- 50 N s Correct answer.
- 0.005 N s
Explanation
Impulse is the product of force and the time for which it acts: impulse = F × t = 100 × 0.5 = 50 N s. This impulse equals the change in momentum of the body.
Question 16Mechanics
A uniform metre rule is pivoted at its centre and balances horizontally. A 2 N weight hangs 20 cm to the left of the pivot. Where must a 4 N weight be hung to keep the rule in equilibrium?
- 20 cm to the right of the pivot
- 10 cm to the right of the pivot Correct answer.
- 5 cm to the right of the pivot
- 40 cm to the right of the pivot
Explanation
By the principle of moments, the anticlockwise moment must equal the clockwise moment: 2 × 20 = 4 × d. Hence d = 40/4 = 10 cm to the right of the pivot.
Question 17Mechanics
A body is in equilibrium under the action of three coplanar forces. Which condition must be satisfied?
- Both the vector sum of the forces and the sum of moments about any point are zero Correct answer.
- Only the vector sum of the forces is zero
- The vector sum of the forces must be non-zero to balance the moments
- Only the sum of moments about the centre of mass is zero
Explanation
For complete equilibrium, both translational and rotational conditions must hold. The resultant force must vanish so there is no linear acceleration, and the net moment about any point must vanish so there is no angular acceleration.
Question 18Mechanics
The work done in lifting a 10 kg mass through a vertical height of 2 m at constant speed is (take g = 10 m/s²)
- 20 J
- 100 J
- 50 J
- 200 J Correct answer.
Explanation
The lifting force must equal the weight, mg = 100 N, and the displacement is 2 m in the direction of the force. Work = force × distance = 100 × 2 = 200 J.
Question 19Mechanics
A machine raises a load of 500 N through 4 m in 10 s. If the power input to the machine is 250 W, what is its efficiency?
- 80% Correct answer.
- 20%
- 50%
- 125%
Explanation
Useful work output = 500 × 4 = 2000 J, so useful power output = 2000/10 = 200 W. Efficiency = (200/250) × 100% = 80%.
Question 20Mechanics
A spring obeys Hooke's law. When a force of 12 N extends it by 4 cm, what force is needed to extend it by 10 cm within the elastic limit?
- 3 N
- 30 N Correct answer.
- 48 N
- 24 N
Explanation
Hooke's law states F = kx, so the extension is proportional to the force. The spring constant is k = 12/0.04 = 300 N/m, and the force for 0.10 m is 300 × 0.10 = 30 N.
Question 21Mechanics
A body of mass 4 kg moves at 5 m/s. What is its kinetic energy?
- 100 J
- 50 J Correct answer.
- 10 J
- 20 J
Explanation
Kinetic energy is given by KE = ½mv². Substituting gives KE = ½ × 4 × 5² = 50 J.
Question 22Mechanics
A ball is projected horizontally at 15 m/s from a cliff 20 m high. Taking g = 10 m/s² and neglecting air resistance, how long does it take to reach the ground?
- 2.0 s Correct answer.
- 4.0 s
- 1.5 s
- 0.75 s
Explanation
The vertical motion is independent of the horizontal motion and starts from rest vertically. Using h = ½gt² gives 20 = ½ × 10 × t², so t² = 4 and t = 2.0 s.
Question 23Mechanics
A car of mass 1000 kg travelling at 20 m/s brakes and stops in a distance of 50 m. What is the magnitude of the average braking force?
- 2000 N
- 8000 N
- 4000 N Correct answer.
- 1000 N
Explanation
The initial kinetic energy is ½ × 1000 × 20² = 200 000 J, and this is removed by the braking force over 50 m. Thus F = 200 000/50 = 4000 N.
Question 24Mechanics
Two bodies of masses 3 kg and 1 kg move towards each other with speeds 2 m/s and 4 m/s respectively. They collide and stick together. What is the velocity of the combined body?
- 0.5 m/s in the direction of the 3 kg body Correct answer.
- 1.0 m/s in the direction of the 1 kg body
- 2.5 m/s in the direction of the 3 kg body
- 0.5 m/s in the direction of the 1 kg body
Explanation
Taking the 3 kg direction as positive, total momentum = 3 × 2 − 1 × 4 = 2 kg m/s. The combined mass is 4 kg, so v = 2/4 = 0.5 m/s in the positive direction, that of the 3 kg body.
Question 25Mechanics
A block of mass 5 kg rests on a rough horizontal surface with coefficient of static friction 0.4. A horizontal force is gradually applied. Taking g = 10 m/s², what is the minimum force needed to start the block moving?
- 50 N
- 20 N Correct answer.
- 2 N
- 12.5 N
Explanation
The normal reaction equals the weight, N = mg = 50 N. The maximum static friction is μN = 0.4 × 50 = 20 N, so a force just greater than 20 N is needed to start motion.
Question 26Mechanics
A student measures the length of a pendulum as 0.842 m using a metre rule whose smallest division is 1 mm. Which statement about the recorded value is correct?
- The value has three significant figures and the uncertainty is about 1 cm
- The value has four significant figures and the uncertainty is about 0.1 mm
- The value has three significant figures and the uncertainty is about 1 mm Correct answer.
- The value has four significant figures and the uncertainty is about 1 mm
Explanation
A metre rule with a 1 mm smallest division gives a reading uncertain by roughly half a division, so about 1 mm. The digits 8, 4 and 2 are all meaningful, giving three significant figures; the trailing zero of the centimetre scale is not recorded.
Question 27Mechanics
Which of the following is a vector quantity?
- Mass
- Speed
- Distance
- Displacement Correct answer.
Explanation
A vector needs both magnitude and direction, and displacement is the straight-line change of position with a stated direction. Distance, speed and mass are scalars because they are completely described by magnitude alone.
Question 28Mechanics
A man walks 3 km due east and then 4 km due north. What is the magnitude of his displacement from the starting point?
- 12 km
- 1 km
- 5 km Correct answer.
- 7 km
Explanation
The two legs are perpendicular, so the resultant displacement is found by the Pythagorean theorem: the square root of (3² + 4²) km² equals 5 km. Displacement depends only on the initial and final positions, not on the path taken.
Question 29Mechanics
A body moves along a straight line with uniform velocity. Which statement about the body is correct?
- Its acceleration is zero but a constant net force acts on it
- Its acceleration is zero and the net force on it is zero Correct answer.
- Its acceleration increases steadily while the net force stays constant
- Its acceleration is constant and non-zero while the net force is zero
Explanation
Uniform velocity means both the magnitude and direction of the velocity stay unchanged, so the acceleration is zero. By Newton's second law a zero acceleration requires a zero resultant force, so the forces on the body balance.
Question 30Mechanics
A car travelling at 20 m/s decelerates uniformly and comes to rest in 8 s. What is the magnitude of its deceleration?
- 12 m/s²
- 160 m/s²
- 0.4 m/s²
- 2.5 m/s² Correct answer.
Explanation
Acceleration is the change in velocity divided by the time taken: (0 − 20) m/s over 8 s gives −2.5 m/s², so the deceleration is 2.5 m/s². The negative sign shows the acceleration opposes the motion.
Question 31Mechanics
A stone is dropped from rest from a tower and reaches the ground in 3 s. Taking g = 10 m/s² and neglecting air resistance, how tall is the tower?
- 90 m
- 15 m
- 30 m
- 45 m Correct answer.
Explanation
For a body released from rest, the distance fallen is ½gt². Substituting gives ½ × 10 × 3² = 45 m, and the mass of the stone does not affect the result when air resistance is neglected.
Question 32Mechanics
A projectile is launched with a velocity that has a horizontal component of 12 m/s and a vertical component of 16 m/s. Neglecting air resistance, what is the speed of the projectile at the highest point of its path?
- 16 m/s
- 20 m/s
- 12 m/s Correct answer.
- 0 m/s
Explanation
At the highest point the vertical component of velocity is zero, but the horizontal component is unaffected because no horizontal force acts. The speed there therefore equals the horizontal component, 12 m/s.
Question 33Mechanics
A body moves in a straight line with an acceleration that is always directed opposite to its velocity. Which statement describes the motion?
- The body reverses its direction of motion immediately
- The body moves with constant velocity
- The speed increases while the velocity changes at a constant rate
- The speed decreases, but the velocity need not change at a constant rate Correct answer.
Explanation
Acceleration directed opposite to velocity reduces the magnitude of the velocity, so the body slows down while moving. The stem specifies the direction of acceleration but not its magnitude, so the velocity need not change at a constant rate.
Question 34Mechanics
A body of weight 60 N rests on a horizontal floor. A horizontal force of 15 N is applied but the body remains at rest. What is the magnitude of the friction force acting on the body?
- 0 N
- 15 N Correct answer.
- 45 N
- 60 N
Explanation
While the body stays at rest, the static friction force adjusts to balance the applied horizontal force exactly. Hence friction equals 15 N and acts opposite to the applied force; the 60 N weight is balanced by the normal reaction.
Question 35Mechanics
A uniform beam of negligible weight is pivoted at its centre. A 6 N weight hangs 0.30 m to the left of the pivot. Where must a 9 N weight be hung to keep the beam horizontal?
- 0.10 m to the right of the pivot
- 0.20 m to the right of the pivot Correct answer.
- 0.45 m to the right of the pivot
- 0.30 m to the right of the pivot
Explanation
For rotational equilibrium the clockwise and anticlockwise moments about the pivot must be equal: 6 N × 0.30 m = 1.8 N m. Dividing by 9 N gives 0.20 m on the opposite side of the pivot.
Question 36Mechanics
A body of mass 2 kg moving at 3 m/s collides head-on with a body of mass 4 kg moving at 1.5 m/s in the opposite direction. They stick together. What is the velocity of the combined body?
- 4.5 m/s in the direction of the 2 kg body
- 0 m/s Correct answer.
- 1 m/s in the direction of the 2 kg body
- 2 m/s in the direction of the 4 kg body
Explanation
Taking the 2 kg body's direction as positive, total momentum before impact is (2 × 3) − (4 × 1.5) = 0 kg m/s. Since momentum is conserved and the combined mass is non-zero, the combined velocity must be zero.
Question 37Mechanics
A pump raises 200 kg of water through a height of 5 m every minute. Taking g = 10 m/s², what is the useful output power of the pump?
- 1000 W
- 2000 W
- 10 W
- 167 W Correct answer.
Explanation
Useful work done is mgh = 200 × 10 × 5 = 10 000 J, delivered in 60 s. Power is work divided by time, giving 10 000/60 ≈ 167 W, which is the rate of gain of potential energy of the water.
Question 38Mechanics
A block slides down a rough inclined plane at constant speed. Which statement about the energy changes is correct?
- The loss of gravitational potential energy equals the work done against friction Correct answer.
- The total mechanical energy of the block increases as it descends
- The loss of gravitational potential energy equals the gain in kinetic energy
- Both potential and kinetic energy decrease as the block descends
Explanation
Constant speed means the kinetic energy does not change, so the decrease in potential energy is entirely dissipated as work done against friction. The total mechanical energy therefore decreases by that amount.
Question 39Mechanics
A satellite moves in a circular orbit around a planet. The gravitational force provides the centripetal force. If the orbital radius is increased to four times its original value, what happens to the orbital speed?
- It becomes half the original value Correct answer.
- It becomes one quarter of the original value
- It becomes twice the original value
- It stays unchanged
Explanation
Equating gravitational force to centripetal force gives v² = GM/r, so the speed is inversely proportional to the square root of the radius. Quadrupling r reduces v by a factor of two, since the square root of 4 is 2.
Question 40Mechanics
A uniform metre rule of weight 2.0 N is pivoted at its centre. A 6.0 N weight is hung 20 cm from the pivot on the left side. At what distance from the pivot on the right side must a 4.0 N weight be hung so that the rule balances horizontally?
- 15 cm
- 20 cm
- 40 cm
- 30 cm Correct answer.
Explanation
For a body in rotational equilibrium the total clockwise moment about the pivot equals the total anticlockwise moment. The 6.0 N weight gives an anticlockwise moment of 6.0 × 0.20 = 1.2 N m. If the 4.0 N weight is hung at distance d, then 4.0 × d = 1.2, giving d = 0.30 m = 30 cm. The weight of the uniform rule acts at the pivot, so it produces no moment and does not affect the answer.
Question 41Thermodynamics and Kinetic Theory
A fixed mass of ideal gas is heated at constant volume. Which quantity must increase?
- The average kinetic energy of the gas molecules Correct answer.
- The volume occupied by the gas
- The mass of each gas molecule
- The number of gas molecules
Explanation
At constant volume the gas does no work, so all heat supplied raises internal energy and therefore temperature. For an ideal gas, temperature is directly proportional to mean translational kinetic energy, so heating increases it. Molecule count and molecular mass are fixed properties of the sample.
Question 42Thermodynamics and Kinetic Theory
Which statement correctly describes the pressure exerted by a gas on the walls of its container, according to kinetic theory?
- It arises from the rate of change of momentum of molecules colliding with the walls Correct answer.
- It arises from static electric repulsion between molecules and the walls
- It arises from the weight of the gas column above the walls
- It arises from molecules sticking permanently to the walls
Explanation
In kinetic theory, molecules collide elastically with the wall and rebound, so their momentum reverses. The rate of change of momentum per unit area gives the force per unit area, which is the pressure. The other descriptions contradict the assumptions of kinetic theory.
Question 43Thermodynamics and Kinetic Theory
A gas is compressed slowly at constant temperature. Which statement about the gas is correct?
- Its pressure decreases because the molecules move more slowly
- Its internal energy increases because work is done on it
- Its pressure increases because the molecules strike the walls more frequently per unit area Correct answer.
- Its temperature rises because the molecules become more energetic
Explanation
At constant temperature the mean molecular speed is unchanged, but the same number of molecules occupies a smaller volume. Collisions with unit area of wall therefore occur more often, so pressure rises, consistent with Boyle's law. Internal energy of an ideal gas depends only on temperature and stays constant.
Question 44Thermodynamics and Kinetic Theory
The absolute temperature of an ideal gas is doubled while its volume is kept constant. The root-mean-square speed of its molecules becomes
- √2 times its original value Correct answer.
- 2 times its original value
- unchanged
- 4 times its original value
Explanation
Root-mean-square speed is proportional to the square root of absolute temperature, since mean kinetic energy equals (3/2)kT. Doubling T multiplies the speed by the square root of 2. It does not double, because kinetic energy depends on the square of speed.
Question 45Thermodynamics and Kinetic Theory
Which of the following is an assumption of the kinetic theory of an ideal gas?
- Collisions between molecules are perfectly elastic Correct answer.
- Molecules move with widely different speeds at absolute zero
- Molecules attract one another strongly at all separations
- The volume of the molecules is a large fraction of the container volume
Explanation
Kinetic theory assumes molecules collide elastically so no kinetic energy is lost in collisions. It also assumes negligible intermolecular forces and negligible molecular volume compared with the container. At absolute zero the model gives zero mean kinetic energy.
Question 46Thermodynamics and Kinetic Theory
In an isothermal process for an ideal gas, the heat absorbed by the gas is equal to
- zero in all cases
- the product of pressure and volume
- the work done by the gas Correct answer.
- the change in internal energy of the gas
Explanation
The first law states that heat supplied equals change in internal energy plus work done by the gas. For an ideal gas at constant temperature the internal energy does not change, so the heat absorbed equals the work done by the gas. This is why the process can absorb heat while temperature stays fixed.
Question 47Thermodynamics and Kinetic Theory
A gas in a cylinder is heated so that it expands and pushes a piston outward. Which energy transfer is described by the gas doing work on the surroundings?
- The gas pressure equals atmospheric pressure
- The gas transfers heat through the cylinder walls
- The gas molecules increase their average speed
- The gas exerts a force on the piston and moves it through a distance Correct answer.
Explanation
Work is done when a force moves its point of application through a distance. The gas pressure acts on the piston area, producing a force that moves the piston, so the gas does work on the surroundings. Heating and speed changes involve energy transfer by other means.
Question 48Thermodynamics and Kinetic Theory
A sealed rigid container holds a gas at constant temperature. According to the kinetic theory, the pressure of the gas is independent of
- the mean square speed of the molecules
- the mass of an individual molecule only when temperature and number density are fixed Correct answer.
- the number of molecules per unit volume
- the absolute temperature of the gas
Explanation
The kinetic equation gives pressure as one third of the product of number density, molecular mass and mean square speed. If temperature and number density are fixed, the mean square speed is fixed, but pressure still depends on molecular mass. The listed quantities all enter the pressure relation directly, so the statement about independence is the only defensible one.
Question 49Thermodynamics and Kinetic Theory
A fixed mass of gas at constant pressure is cooled from 300 K to 150 K. Its volume becomes
- one quarter of its original volume
- twice its original volume
- half of its original volume Correct answer.
- unchanged
Explanation
Charles's law states that at constant pressure the volume of a fixed mass of gas is directly proportional to absolute temperature. Halving the absolute temperature therefore halves the volume. Using Celsius temperatures instead would give a wrong result, so absolute temperatures must be used.
Question 50Thermodynamics and Kinetic Theory
The pressure of a fixed mass of gas is doubled while its absolute temperature is also doubled. The volume of the gas
- is halved
- is doubled
- remains unchanged Correct answer.
- is quadrupled
Explanation
The combined gas law gives PV/T constant for a fixed mass. Doubling both P and T leaves V unchanged because the two effects cancel. Checking the ratio P/T shows it is unchanged, so volume must stay the same.