Question

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:

• A. 3
• B. 6
• C. 5
• D. 4

Answer 1

The Correct Option is C

To solve this problem, we need to determine the acceleration of the block when struck by the jet of water.

Given data:

• Mass of the block, m = 2 \, \text{kg}
• Rate of water mass flow, \dot{m} = 1 \, \text{kg/s}
• Velocity of water jet, v = 10 \, \text{m/s}

The force exerted by the water jet on the block can be calculated using the formula for force due to a change in momentum:

F = \dot{m} \times v

Substituting the given values, we get:

F = 1 \, \text{kg/s} \times 10 \, \text{m/s} = 10 \, \text{N}

Using Newton's second law, the acceleration a of the block is given by:

F = m \times a

Solving for a:

a = \frac{F}{m} = \frac{10 \, \text{N}}{2 \, \text{kg}} = 5 \, \text{ms}^{-2}

Hence, the initial acceleration of the block is 5 ms^-2.