Free Force and Motion MCQs with Answers

31. The momentum of a body of mass 4 kg moving at 5 m per second is

• A. 20 kg m per second
• B. 0.8 kg m per second
• C. 50 kg m per second
• D. 9 kg m per second

Explanation: Momentum is mass multiplied by velocity, so 4 multiplied by 5 gives 20 kg m per second in the direction of motion. Its kinetic energy would be half times 4 times 25, that is 50 J, which is the trap in the third option. Momentum is a vector while kinetic energy is a scalar.

32. Friction between two surfaces in contact depends on

• A. the area of contact only
• B. the normal force pressing them together and the nature of the surfaces
• C. the speed only, in all cases
• D. the volume of the bodies

Explanation: Limiting friction is the coefficient of friction multiplied by the normal reaction, and to a good approximation it is independent of the apparent area of contact, which surprises most students. Pressing harder or roughening the surfaces increases it. Kinetic friction is usually slightly less than the maximum static friction, which is why a pushed object suddenly lurches once it starts to slide.

33. If the horizontal range of a projectile becomes half of its maximum possible horizontal range, the probable angle of projection is:

• A. 15 degrees
• B. 30 degrees
• C. 45 degrees
• D. 60 degrees

Explanation: Range is proportional to sin of twice the angle and is greatest at 45 degrees, where sin 90 equals 1, so half the maximum range needs sin 2 theta equal to 0.5, giving 2 theta equal to 30 degrees and theta equal to 15 degrees. The other solution is 75 degrees, since the two angles are complementary. Answering 30 degrees comes from halving the angle instead of the sine.

34. A ball is thrown into the air with certain velocity v making an angle with horizontal. If air resistance is neglected, then at maximum height its velocity is:

• A. Equal to initial velocity
• B. Half of initial velocity
• C. Equal to zero
• D. Minimum but not zero

Explanation: At the top the vertical component has fallen to zero, but the horizontal component is unchanged throughout the flight because no horizontal force acts, so the ball still moves horizontally at v cos theta. The speed is therefore at its minimum for the flight yet not zero, which is the distinction being tested. Only a ball thrown straight up would momentarily stop.

35. A cannon is placed on a smooth surface. When it fires a shell, the cannon moves backward. This recoil occurs due to:

• A. Law of conservation of energy
• B. Backward thrust of the gases
• C. Newton's third law of motion
• D. Newton's first law of motion

Explanation: The cannon pushes the shell forward and the shell pushes the cannon back with an equal and opposite force, which is the third law, and the same situation expressed as conservation of momentum gives the recoil velocity. Because the cannon is far more massive than the shell, its backward speed is correspondingly small. Energy is conserved too, but it does not by itself explain the direction of the motion.

36. A projectile is launched in air with certain angle; its velocity is maximum at:

• A. Point of projection
• B. Highest point
• C. Between launching and highest point
• D. At all points

Explanation: The vertical component decreases as the projectile rises and is regained on the way down, so the speed is greatest at launch and again on landing at the same height, and least at the top where only the horizontal component remains. Neglecting air resistance, the landing speed equals the launch speed. This follows directly from energy conservation, since the kinetic energy is greatest where the height is least.

37. If a body having mass m1 (2 kg) moving with 5 m/s approaches another mass m2 (3 kg) with speed of 1 m/s in same direction, relative speed of approach is 4 m/s. Relative speed of separation after collision will be:

• A. 4 m/s
• B. 2 m/s
• C. 6 m/s
• D. Depends on masses

Explanation: For a perfectly elastic collision the relative speed of separation equals the relative speed of approach, whatever the masses, which follows from conserving both momentum and kinetic energy. So the 4 m per second closing speed becomes a 4 m per second separating speed. In an inelastic collision the separation speed would be smaller, and in a perfectly inelastic one it would be zero.