Question

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

Options

• 3

• 6

• 5

• 4

Answer 1

5

Explanation:

As water ejected by jet strikes the block, it imparts momentum to the block

⇒ Change in momentum of water jet in 1 s = Momentum gained by block in 1 s.

⇒ Change in momentum of jet in second = Mass of jet ejected in 1 second × change in velocity

= 1 `("kg")/"s"` × (10 - 0)

= 10 kg m/s

⇒ Momentum gained by block = 10 kg m/s

By Newton’s II law of motion ⇒ F = Rate of change of momentum

= `"Δp"/"Δt"`

F = `(10  kg  "m"//"s")/(1"s")`

= 10 kg `m/s^2` = 10N

Thus, 10 N force acts on the block

By F = ma

a = `"F"/"m" = 10/2` = 5m/s²