AIPMT 2008 Questions on Newton’s Laws of Motion

The following questions which appeared in All India Pre-Medical/Pre-Dental Entrance Examination (AIPMT) 2008 are worth noting:

(i) A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is

(1) 80 ms^–1

(2) 40 ms^–1

(3) 120 ms^–1

(4) 100 ms^–1

This question is meant for testing your grasp of the laws of conservation of momentum and energy. If v and V represent the initial velocity of the shell of mass m and the recoil velocity of the gun of mass M respectively, we have (from the law of conservation of momentum)

mv + MV = 0 from which V = – (m/M)v = – (0.2/4)v = – v/20 ms^–1

[The negative sign shows that the recoil velocity of the gun is opposite to the velocity of the shell].

The energy of the explosion is used to impart kinetic energy to the shell and the gun so that we have

½ (mv² + MV²) = 1.05×10³

Or, ½ [0.2 v² + (4v²/400 )] = 1.05×10³

This gives v² = 10⁴ so that v = 100 ms^–1.

(ii) Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v ms^–1 will be

(1) 2Mv newton

(2) Mv/2 newton

(3) zero

(4) Mv newton

Since there is a time rate of change of momentum equal to Mv per second, the force required is Mv Newton.