A body of mass 5 ~kg moving with a speed of 1.5 ~m / s on a...

A body of mass

5 \mathrm{~kg}

moving with a speed of

1.5 \mathrm{~m} / \mathrm{s}

on a horizontal smooth surface collides with a nearly weightless spring of force constant

k=5 \mathrm{~N} / \mathrm{m}

. The maximum compression of the spring would be A body of mass 5 ~kg moving with a speed of 1.5 ~m / s on a horizontal smooth surface collides with a nearly weightless

A body of mass 5 ~kg moving with a speed of 1.5 ~m / s on a horizontal smooth surface collides with a nearly weightless

Options

A $0.5 \mathrm{~m}$
B $0.15 \mathrm{~m}$
C $1.5 \mathrm{~m}$
D $0.12 \mathrm{~m}$

Correct answer

C. $1.5 \mathrm{~m}$

Step-by-step solution

At maximum compression the whole kinetic energy of ball = potential energy of spring.

\begin{aligned} & \frac{1}{2} m v^2=\frac{1}{2} k x^2 \Rightarrow x=v \sqrt{\frac{m}{k}} \\ & x=1.5 \times \sqrt{\frac{5}{5}}=1.5 \mathrm{~m}\end{aligned}

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