A ball of mass 4 kg, moving with a velocity $10 \mathrm{~ms}^{-1}$, collides with a spring of length 8 m and force constant $100 \mathrm{Nm}^{-1}$. The length of compressed spring is x m. The value of x, to the nearest integer, is ____

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Work, Power & Energy

A ball of mass 4 kg, moving with a velocity

10 ms^{- 1}

, collides with a spring of length 8 m and force constant

100 Nm^{- 1}

. The length of compressed spring is x m. The value of x, to the nearest integer, is ____

Answer: 6

Solution

Using conservation of energy, the kinetic energy of the ball is converted to elastic potential energy of the spring.

\frac{1}{2} m v^{2} = \frac{1}{2} k (Δ l)^{2}

, where

Δ l

is the compression. We have

\frac{1}{2} \times 4 \times 1 0^{2} = \frac{1}{2} \times 100 \times (Δ l)^{2}

, giving

200 = 50 (Δ l)^{2}

, so

(Δ l)^{2} = 4

and

Δ l = 2

m. The compressed length is

x = 8 - 2 = 6

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Integer answer

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