Free Force and Motion MCQs with Answers

21. A body of mass 2 kg moving at 3 m per second collides and sticks to a stationary body of mass 4 kg. Their common velocity is

• A. 1 m per second
• B. 1.5 m per second
• C. 0.5 m per second
• D. 3 m per second

Explanation: Total momentum before is 2 multiplied by 3, that is 6 kg m per second, and the combined mass afterwards is 6 kg, so the common velocity is 1 m per second. The kinetic energy falls from 9 J to 3 J, the difference going into heat and deformation. Momentum is conserved even though energy is not.

22. In an elastic collision between two bodies of equal mass, one moving and one at rest

• A. they stick together
• B. the moving body stops and the stationary one moves off with the original velocity
• C. both move off at half the original velocity
• D. the moving body rebounds

Explanation: Conserving both momentum and kinetic energy for equal masses gives a complete exchange of velocities, which is what makes the Newton's cradle behave as it does and why a cue ball stops dead on a full head on strike. Sticking together would violate energy conservation for an elastic collision. Both moving off at half speed conserves momentum but not kinetic energy.

23. A projectile launched at angle theta has its maximum range when theta equals

• A. 30 degrees
• B. 45 degrees
• C. 60 degrees
• D. 90 degrees

Explanation: Range is proportional to sin 2 theta, which is maximum when 2 theta is 90 degrees, that is at 45 degrees, assuming level ground and no air resistance. Angles of 30 and 60 degrees give the same range as each other, since their doubles are supplementary. At 90 degrees the projectile goes straight up and the range is zero.

24. For a projectile in flight, neglecting air resistance, the horizontal component of velocity

• A. increases steadily
• B. decreases steadily
• C. stays constant, because no horizontal force acts
• D. becomes zero at the highest point

Explanation: Gravity acts vertically only, so the horizontal motion is uniform while the vertical motion is uniformly accelerated, and treating the two independently is the key to every projectile problem. At the highest point the vertical component is zero but the horizontal component is unchanged, so the speed there is not zero. This is why a bomb released from a moving aircraft continues to travel forward with it.

25. A stone is dropped from rest and falls freely for 3 seconds. Taking g as 10 m per second squared, the distance fallen is

• A. 15 m
• B. 30 m
• C. 45 m
• D. 90 m

Explanation: Using s equals half g t squared, the distance is half multiplied by 10 multiplied by 9, giving 45 m. The value 30 m is the velocity after 3 seconds in metres per second, offered as a distractor. Distance in free fall grows with the square of the time, not in proportion to it.

26. A car accelerates uniformly from 10 m per second to 30 m per second in 5 seconds. Its acceleration is

• A. 2 m per second squared
• B. 4 m per second squared
• C. 6 m per second squared
• D. 8 m per second squared

Explanation: Acceleration is the change in velocity divided by the time, so 20 divided by 5 gives 4 m per second squared. Dividing the final velocity by the time instead gives 6, a common slip. The distance covered in that time would be the average velocity of 20 multiplied by 5, that is 100 m.

27. Distance differs from displacement in that distance

• A. is a vector and displacement is a scalar
• B. is the total path length travelled, while displacement is the straight line change in position
• C. is always smaller than displacement
• D. is measured in different units

Explanation: Walking once round a circular track leaves the displacement at zero while the distance equals the circumference, so distance can exceed displacement but never be less than it. Distance is the scalar and displacement the vector, which is the reverse of the first option. Both are measured in metres.

28. A body moving with constant speed in a circle has

• A. constant velocity
• B. zero acceleration
• C. changing velocity and therefore acceleration
• D. no force acting on it

Explanation: Velocity is a vector, so a continuous change of direction is a change of velocity even at constant speed, and the acceleration points towards the centre. A net force must therefore act, supplied by tension, friction or gravity depending on the situation. Constant speed and constant velocity are not the same thing.

29. The apparent weight of a person standing in a lift accelerating upwards is

• A. greater than their true weight
• B. less than their true weight
• C. equal to their true weight
• D. zero

Explanation: The floor must both support the weight and supply the extra upward force to accelerate the person, so the normal reaction, which is what the scales read, is m times g plus a. Accelerating downwards makes the reading smaller, and in free fall it drops to zero, which is the weightlessness astronauts experience. The true weight, mg, is unchanged throughout.

30. A rocket moves forward in the vacuum of space because

• A. the exhaust gases push against the air behind it
• B. the momentum carried away by the exhaust gases is balanced by an equal forward momentum of the rocket
• C. gravity pulls it forward
• D. it becomes lighter as fuel burns

Explanation: Conservation of momentum, equivalently Newton's third law, means expelling mass backwards at speed drives the rocket forwards, and no surrounding medium is needed. This is why rockets work best in a vacuum, where there is no air resistance. Losing mass does help the acceleration but is not the source of the thrust.