A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs⁻¹ and at a speed of 10 ms⁻¹. Then, the initial acceleration of the block, in ms⁻², will be :

Solution

Physics sir · 3 steps

The jet pushes with a force equal to the momentum of water it stops each second, so find that first.

1. Force from the jet. Each second, 1 kg of water arrives at 10 m s⁻¹ and loses its horizontal speed on hitting the block. By Newton's second law, the force equals the rate at which this momentum is removed.

   F = dm/dt v = 1 kg s⁻¹ × 10 m s⁻¹ = 10 N

2. Why initial matters. At the start the block is at rest, so the water hits it at the full 10 m s⁻¹. Once the block moves, the relative speed drops and so does the force.
3. So. The plane is frictionless, so this 10 N is the only horizontal force. a = F/m = 10/2 = 5 m s⁻², option (c).

The idea to keep. A jet or stream exerts a force equal to the momentum it delivers per second: F = dm/dt vᵣₑₗ. Use the relative speed, and double it only if the stream bounces straight back.

Answer from the NTA final answer key. Solution by PrepWiser.