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Question 1Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A car moves along a straight road with constant velocity of 20 m/s. What distance does it travel in 15 s?
- 150 m
- 300 m Correct answer.
- 75 m
- 1.33 m
Explanation
For constant velocity the displacement is the product of speed and time, d = v·t. Substituting gives 20 m/s × 15 s = 300 m.
Question 2Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A body starts from rest and moves with constant acceleration of 4 m/s². What is its speed after 6 s?
- 144 m/s
- 1.5 m/s
- 24 m/s Correct answer.
- 10 m/s
Explanation
For constant acceleration from rest, v = a·t. Thus v = 4 m/s² × 6 s = 24 m/s.
Question 3Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A ball is thrown vertically upward. At the highest point of its path, what is true of its acceleration (ignoring air resistance)?
- It equals g directed downward Correct answer.
- It equals g directed upward
- It is zero
- It is directed upward but smaller than g
Explanation
Gravity acts throughout the flight, so the acceleration is constant at g pointing downward. Only the velocity becomes zero at the top, not the acceleration.
Question 4Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A projectile is launched horizontally from a height. Neglecting air resistance, how does its horizontal velocity component change during the flight?
- It first decreases then increases
- It decreases steadily
- It increases steadily
- It stays constant Correct answer.
Explanation
No horizontal force acts once the projectile is in flight, so the horizontal component of velocity remains constant. Only the vertical component changes, due to gravity.
Question 5Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A block of mass 5 kg rests on a horizontal table. What is the magnitude of the normal force exerted by the table on the block? (Take g = 10 m/s².)
- 5 N
- 50 N Correct answer.
- 500 N
- 0.5 N
Explanation
In vertical equilibrium the normal force balances the weight, N = m·g. Thus N = 5 kg × 10 m/s² = 50 N.
Question 6Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
Two forces of 3 N and 4 N act at right angles at a point. What is the magnitude of their resultant?
- 5 N Correct answer.
- 12 N
- 1 N
- 7 N
Explanation
Perpendicular vectors add by the Pythagorean theorem: R = √(3² + 4²) = √25 = 5 N.
Question 7Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A body of mass 2 kg experiences a net force of 6 N. What is its acceleration?
- 12 m/s²
- 8 m/s²
- 0.33 m/s²
- 3 m/s² Correct answer.
Explanation
Newton's second law gives a = F/m. Thus a = 6 N / 2 kg = 3 m/s².
Question 8Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
Two skaters push off from each other on frictionless ice and move apart. Which statement describes the forces they exert on each other?
- Equal in magnitude and same in direction
- Equal in magnitude and opposite in direction Correct answer.
- Larger on the lighter skater
- Larger on the heavier skater
Explanation
By Newton's third law the mutual forces are an action-reaction pair: equal magnitude and opposite direction, regardless of mass.
Question 9Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A satellite orbits Earth in a circular orbit. What provides the centripetal force keeping it in orbit?
- Gravitational attraction toward Earth Correct answer.
- Air pressure on the satellite
- The rotation of the Earth
- The satellite's tangential velocity
Explanation
The only significant force on an orbiting satellite is gravity, directed toward Earth's center, which acts as the centripetal force.
Question 10Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A uniform beam is pivoted at its center and is in equilibrium. A 10 N weight hangs 0.2 m to the left of the pivot. Where must a 5 N weight be placed to balance it?
- 0.2 m to the right of the pivot
- 0.8 m to the right of the pivot
- 0.1 m to the right of the pivot
- 0.4 m to the right of the pivot Correct answer.
Explanation
Equilibrium of moments requires F₁d₁ = F₂d₂. Solving 10 N × 0.2 m = 5 N × d gives d = 0.4 m.
Question 11Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A solid cylinder and a hollow cylinder of the same mass and radius roll without slipping down an incline from rest. Which reaches the bottom first?
- They arrive together
- It depends on the incline length
- The hollow cylinder
- The solid cylinder Correct answer.
Explanation
The solid cylinder has a smaller moment of inertia factor, so more of its energy goes into translation and it accelerates faster. The hollow cylinder stores more energy in rotation.
Question 12Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A block slides down a rough incline at constant speed. Which statement about the forces is correct?
- The component of gravity along the incline equals the friction force Correct answer.
- The friction force exceeds the gravity component
- No friction acts because the speed is constant
- The normal force equals the weight
Explanation
Constant velocity means zero net force along the incline, so the downhill gravity component is balanced by kinetic friction. The normal force equals only the perpendicular component of weight.
Question 13Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A 60 kg person stands in a lift accelerating upward at 2 m/s². What is the normal force from the floor? (Take g = 10 m/s².)
- 480 N
- 720 N Correct answer.
- 600 N
- 120 N
Explanation
Newton's second law gives N − mg = ma, so N = m(g + a) = 60 × 12 = 720 N.
Question 14Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A ball of mass 0.5 kg hits a wall horizontally at 10 m/s and rebounds at 6 m/s. If the contact lasts 0.02 s, what is the magnitude of the average force on the ball?
- 40 N
- 400 N Correct answer.
- 200 N
- 100 N
Explanation
Take the rebound direction as positive; the change in momentum is m(v₂ − v₁) = 0.5 × (6 − (−10)) = 8 kg·m/s. Dividing by 0.02 s gives 400 N.
Question 15Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A block of wood floats in water with part of its volume above the surface. What is the magnitude of the buoyant force?
- Equal to the weight of the block Correct answer.
- Equal to the atmospheric pressure times the area
- Equal to the weight of the whole block's volume of water
- Greater than the weight of the block
Explanation
A floating body is in equilibrium, so the buoyant force equals its weight. The buoyant force also equals the weight of the displaced water, which is only part of the block's volume.
Question 16Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
Water flows through a horizontal pipe that narrows to half its original cross-sectional area. How does the flow speed in the narrow section compare with the wide section?
- It is twice as large Correct answer.
- It is half as large
- It is four times as large
- It is the same
Explanation
Continuity for an incompressible fluid gives A₁v₁ = A₂v₂. Halving the area therefore doubles the speed.
Question 17Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A body moves in a circle of radius 2 m at a constant speed of 6 m/s. What is the magnitude of its centripetal acceleration?
- 18 m/s² Correct answer.
- 3 m/s²
- 12 m/s²
- 72 m/s²
Explanation
Centripetal acceleration is a = v²/r. Thus a = 36 / 2 = 18 m/s².
Question 18Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A stone is dropped from rest and falls freely for 3 s. How far does it fall? (Take g = 10 m/s².)
- 30 m
- 90 m
- 45 m Correct answer.
- 15 m
Explanation
For free fall from rest, s = ½gt². Thus s = ½ × 10 × 9 = 45 m.
Question 19Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
Two point masses are separated by a distance r. If the distance between them is doubled while the masses are unchanged, the gravitational force becomes
- Four times the original
- One quarter of the original Correct answer.
- One half of the original
- Twice the original
Explanation
Newton's law of gravitation gives F proportional to 1/r². Doubling r multiplies the force by 1/4.
Question 20Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A flywheel of moment of inertia 4 kg·m² is acted on by a net torque of 12 N·m. What is its angular acceleration?
- 0.33 rad/s²
- 3 rad/s² Correct answer.
- 48 rad/s²
- 8 rad/s²
Explanation
The rotational analogue of Newton's second law is τ = Iα, so α = τ/I = 12/4 = 3 rad/s².
Question 21Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A 2 kg mass moving at 3 m/s collides head-on with a stationary 1 kg mass and they stick together. What is their common speed after the collision?
- 2 m/s Correct answer.
- 3 m/s
- 1.5 m/s
- 0.75 m/s
Explanation
Momentum is conserved in a perfectly inelastic collision: m₁v₁ = (m₁ + m₂)v. Thus v = 6/3 = 2 m/s.
Question 22Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A uniform rod of length L and mass M is pivoted at one end. What is its moment of inertia about that end?
- (1/3)ML² Correct answer.
- (1/12)ML²
- ML²
- (1/2)ML²
Explanation
For a rod about an end the moment of inertia is (1/3)ML². The value (1/12)ML² applies about the center of mass.
Question 23Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A block slides down a frictionless incline of height h starting from rest. Its speed at the bottom depends on
- Only the height h Correct answer.
- The length of the incline
- The angle of the incline
- The mass of the block
Explanation
Energy conservation gives ½mv² = mgh, so v = √(2gh), independent of mass and of the incline geometry. Only the vertical drop matters.
Question 24Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A small body of mass m moves in a circular orbit of radius r around a planet of mass M. Which expression gives its orbital speed?
- √(GMr)
- GM/r²
- √(2GM/r)
- √(GM/r) Correct answer.
Explanation
Setting the gravitational force equal to the required centripetal force, GMm/r² = mv²/r, gives v = √(GM/r).
Question 25Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A uniform solid sphere and a hoop of equal mass and radius start from rest at the same height and roll without slipping down an incline. What is the ratio of the sphere's speed to the hoop's speed at the bottom?
- 1
- √(4/3)
- √(7/5)
- √(10/7) Correct answer.
Explanation
For rolling from rest, v² = 2gh/(1 + I/(mr²)). The sphere has I/(mr²) = 2/5, giving v² = 10gh/7. The hoop has I/(mr²) = 1, giving v² = gh. The ratio is √(10/7).
Question 26Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A car starts from rest and accelerates uniformly at 2 m/s² for 5 s. How far does it travel in this time?
- 50 m
- 10 m
- 25 m Correct answer.
- 20 m
Explanation
For uniform acceleration from rest, s = ½at². Substituting a = 2 m/s² and t = 5 s gives s = ½ × 2 × 25 = 25 m.
Question 27Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A projectile is launched at an angle to the horizontal over level ground with no air resistance. At the highest point of its path, what is true of its acceleration?
- It is zero because the vertical velocity vanishes.
- It points vertically upward with magnitude g.
- It points vertically downward with magnitude g. Correct answer.
- It points horizontally in the direction of motion.
Explanation
The only force acting after launch is gravity, which is constant and vertical. Acceleration therefore equals g downward at every point, including the apex, even though the vertical velocity component is momentarily zero.
Question 28Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A block rests on a horizontal table. Which pair of forces forms an action–reaction pair according to Newton's third law?
- The normal force from the table and the block's push on the table
- The normal force from the table and the block's weight
- The block's weight and the normal force from the table
- The block's weight and the gravitational pull the block exerts on Earth Correct answer.
Explanation
Action–reaction pairs act on different bodies and are of the same type. The block's weight (Earth pulling the block) pairs with the block pulling Earth gravitationally.
Question 29Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A 5 kg block is pulled along a rough horizontal floor by a horizontal force of 30 N. The coefficient of kinetic friction is 0.4. What is the acceleration of the block? (Take g = 10 m/s².)
- 6 m/s²
- 10 m/s²
- 2 m/s² Correct answer.
- 4 m/s²
Explanation
Friction is μmg = 0.4 × 5 × 10 = 20 N, so the net force is 30 − 20 = 10 N. Dividing by mass gives a = 10/5 = 2 m/s².
Question 30Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A 3 kg mass hangs from a rope over a frictionless pulley and is connected to a 5 kg mass resting on a frictionless horizontal table. What is the acceleration of the system? (Take g = 10 m/s².)
- 2 m/s²
- 10 m/s²
- 3.75 m/s² Correct answer.
- 6.25 m/s²
Explanation
The driving force is the hanging weight, 30 N, acting on the total mass of 8 kg. Thus a = 30/8 = 3.75 m/s².
Question 31Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A uniform metre stick of negligible weight is supported at its centre. A 4 N weight hangs 30 cm to the left of the support and a 6 N weight hangs on the right. Where must the 6 N weight be placed for balance?
- 20 cm to the right of the support Correct answer.
- 30 cm to the right of the support
- 45 cm to the right of the support
- 10 cm to the right of the support
Explanation
For rotational equilibrium the moments must be equal: 4 × 30 = 6 × d, giving d = 20 cm.
Question 32Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A uniform solid disc of mass M and radius R rotates about its central axis. What is its moment of inertia?
- MR²
- ⅓MR²
- ⅖MR²
- ½MR² Correct answer.
Explanation
For a uniform solid disc or cylinder about its symmetry axis, I = ½MR². The factor ½ reflects that mass is distributed throughout the cross-section.
Question 33Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A skater spinning with arms outstretched pulls her arms in, reducing her moment of inertia. Assuming no external torque acts, what happens to her angular velocity and rotational kinetic energy?
- Angular velocity increases and kinetic energy increases. Correct answer.
- Angular velocity stays the same and kinetic energy increases.
- Angular velocity decreases and kinetic energy stays the same.
- Angular velocity increases and kinetic energy decreases.
Explanation
Angular momentum L = Iω is conserved, so reducing I raises ω. Kinetic energy ½Iω² = L²/(2I) then increases because I decreases while L is fixed; the extra energy comes from the work done pulling the arms inward.
Question 34Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
Two planets have masses in the ratio 1:4 and radii in the ratio 1:2. What is the ratio of the escape speed from the first planet to that from the second?
- 1:2
- 1:1
- 1:√2 Correct answer.
- 2:1
Explanation
Escape speed is v = √(2GM/R), so v ∝ √(M/R). The ratio is √((1/1)/(4/2)) = √(1/2) = 1/√2.
Question 35Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A satellite is in a circular orbit around Earth. If its orbital radius is increased to four times its original value, by what factor does its orbital period change?
- It becomes 2 times larger.
- It becomes 16 times larger.
- It becomes 4 times larger.
- It becomes 8 times larger. Correct answer.
Explanation
Kepler's third law gives T² ∝ r³, so T ∝ r^{3/2}. With r multiplied by 4, T grows by 4^{3/2} = 8.
Question 36Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A horizontal pipe carries water at 2 m/s where its cross-sectional area is 0.02 m². At a narrower section the area is 0.005 m². What is the speed of the water at the narrow section?
- 0.5 m/s
- 2 m/s
- 8 m/s Correct answer.
- 4 m/s
Explanation
By continuity for an incompressible fluid, A₁v₁ = A₂v₂. Thus v₂ = (0.02 × 2)/0.005 = 8 m/s.
Question 37Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A block of volume 2 × 10⁻³ m³ is fully submerged in a fluid of density 800 kg/m³. What is the buoyant force on it? (Take g = 10 m/s².)
- 20 N
- 160 N
- 8 N
- 16 N Correct answer.
Explanation
Archimedes' principle gives buoyant force equal to the weight of displaced fluid: ρVg = 800 × 2 × 10⁻³ × 10 = 16 N.
Question 38Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A body moves in a straight line such that its velocity–time graph is a straight line passing through the origin with positive slope. What does the area under the graph between t = 0 and t = T represent?
- The rate of change of acceleration
- The acceleration of the body
- The average velocity of the body
- The displacement of the body Correct answer.
Explanation
The area under a velocity–time graph equals the displacement over that interval. For a straight line through the origin the area is a triangle, giving s = ½vT.
Question 39Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A uniform rod of length 2 m and mass 3 kg is pivoted at one end and held horizontally, then released from rest. What is its initial angular acceleration? (Take g = 10 m/s²; I about the end = ML²/3.)
- 15 rad/s² Correct answer.
- 30 rad/s²
- 5 rad/s²
- 7.5 rad/s²
Explanation
The weight acts at the centre, giving torque τ = Mg(L/2). With I = ML²/3, α = τ/I = (3g)/(2L) = 30/4 = 7.5 rad/s².
Question 40Mechanics (kinematics, dynamics, statics, gravitation, rigid bodies, fluids)
A particle moves with simple harmonic motion of amplitude 0.1 m and angular frequency 4 rad/s. What is its maximum speed?
- 0.04 m/s
- 0.8 m/s
- 0.4 m/s Correct answer.
- 2.5 m/s
Explanation
Maximum speed in SHM is v_max = Aω = 0.1 × 4 = 0.4 m/s. This occurs as the particle passes through the equilibrium position.
Question 41Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
A sample of an ideal gas is held at constant temperature while its volume is doubled. What happens to the pressure?
- It is doubled.
- It stays the same.
- It is reduced to one quarter.
- It is halved. Correct answer.
Explanation
Boyle's law states that for a fixed amount of ideal gas at constant temperature, pressure times volume is constant. Doubling the volume therefore halves the pressure.
Question 42Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
The average translational kinetic energy of molecules in an ideal gas depends only on which quantity?
- The mass of each molecule.
- The absolute temperature. Correct answer.
- The pressure of the gas.
- The volume of the container.
Explanation
Equipartition gives the mean translational kinetic energy as (3/2)kT per molecule, which depends only on absolute temperature. Neither molecular mass nor pressure appears in that expression.
Question 43Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
Which statement correctly describes the first law of thermodynamics with the sign convention Q = ΔU + W, where W is work done by the gas?
- Work done on a gas always increases its internal energy by the same amount.
- Heat added to a gas either raises its internal energy or is spent doing work. Correct answer.
- Internal energy can increase without any heat or work exchange.
- Heat and work are state functions that add to give internal energy.
Explanation
The first law expresses energy conservation: heat supplied to the system is partitioned between change of internal energy and work done by the system. Heat and work are process quantities, while internal energy is a state function.
Question 44Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
During a phase change of a pure substance at constant pressure, the temperature remains constant. Why?
- The substance stops absorbing heat once melting begins.
- The pressure increase exactly cancels the temperature rise.
- The supplied energy changes the potential energy of the molecules rather than their mean kinetic energy. Correct answer.
- The molecules lose kinetic energy as fast as they gain it from the surroundings.
Explanation
Latent heat is used to break intermolecular bonds, increasing potential energy while the mean kinetic energy, and hence temperature, stays fixed. Temperature is a measure of mean kinetic energy only.
Question 45Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
An ideal gas undergoes an isothermal expansion. Which quantity is zero for this process?
- The change in entropy of the gas.
- The work done by the gas.
- The change in internal energy. Correct answer.
- The heat absorbed by the gas.
Explanation
For an ideal gas the internal energy depends only on temperature, so an isothermal process has zero change in internal energy. The gas still does work and absorbs an equal amount of heat, and its entropy increases.
Question 46Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
Two containers hold equal numbers of molecules of helium and argon at the same temperature. How do the mean speeds of the molecules compare?
- Argon molecules move faster on average.
- The comparison depends on the pressure.
- Both move at the same mean speed.
- Helium molecules move faster on average. Correct answer.
Explanation
At equal temperature the mean kinetic energy is the same, so mean speed scales as the inverse square root of molecular mass. Helium is lighter than argon, so its molecules move faster.
Question 47Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
Which process is described as adiabatic?
- A process carried out at constant temperature.
- A process in which the gas does no work.
- A process in which no heat is exchanged with the surroundings. Correct answer.
- A process carried out at constant pressure.
Explanation
Adiabatic means no heat transfer, Q = 0, so any change in internal energy comes entirely from work. Constant temperature and constant pressure define isothermal and isobaric processes instead.
Question 48Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
A quantity of heat Q flows from a hot reservoir to a cold reservoir through a conducting rod. What is the entropy change of the universe for this irreversible transfer?
- It is positive. Correct answer.
- It is negative.
- It is zero only if the rod is a perfect conductor.
- It is zero.
Explanation
For spontaneous heat flow from hot (T_h) to cold (T_c), the total entropy change is Q/T_c − Q/T_h, which is positive because T_c < T_h. The second law requires a positive total entropy change for an irreversible process.
Question 49Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
A fixed mass of ideal gas at 300 K and pressure p occupies volume V. It is heated at constant volume to 600 K. What is the new pressure?
- p
- 2p Correct answer.
- p/2
- 4p
Explanation
At constant volume, Gay-Lussac's law gives p/T constant, so doubling the absolute temperature doubles the pressure. The result is 2p.
Question 50Molecular physics and thermodynamics (kinetic theory, ideal gases, heat, phase changes)
One mole of an ideal monatomic gas expands at constant pressure while its temperature rises by 100 K. Taking R = 8.31 J/(mol·K), how much work does the gas do?
- 416 J
- 1247 J
- 831 J Correct answer.
- 2493 J
Explanation
At constant pressure the work is W = pΔV = nRΔT, giving 1 × 8.31 × 100 = 831 J. The heat supplied would be (5/2)RΔT, but only the RΔT part becomes work.