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Properties of Matter question

2022 · 29 Jun · Shift 1 · Q51
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  5. /2022 · 29 Jun · Shift 1 · Q51

Properties of Matter question

2022 · 29 Jun · Shift 1 · Q51

JEE MainPhysicsProperties of MatterMCQ+4 / −1
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 : JEE Main 2022 (Online) 29th June Morning Shift Physics - Properties of Matter Question 166 English
  1. A
    3
  2. B
    6
  3. C
    5
  4. D
    4
View written solutionFree

Correct answer: C

  1. Given data
  • Mass of block: M=2 kgM = 2\,\text{kg}M=2kg
  • Water mass flow rate: m˙=1 kg s−1\dot m = 1\,\text{kg s}^{-1}m˙=1kg s−1
  • Speed of water jet: v=10 m s−1v = 10\,\text{m s}^{-1}v=10m s−1
  • Plane is frictionless.

We need the initial acceleration of the block.

  1. Force exerted by the water jet

The water jet strikes the block and comes to rest along the normal direction relative to the block initially (since the block is initially at rest).

The rate of change of momentum of the water gives the force on the block:

F=m˙ vF = \dot m\, vF=m˙v

Substituting values,

F=1×10=10 NF = 1 \times 10 = 10\,\text{N}F=1×10=10N

  1. Acceleration of the block

Using Newton's second law,

a=FM=102=5 m s−2a = \frac{F}{M} = \frac{10}{2} = 5\,\text{m s}^{-2}a=MF​=210​=5m s−2

  1. Final answer

The initial acceleration of the block is

5 m s−2\boxed{5\,\text{m s}^{-2}}5m s−2​

So, the correct option is C.

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