First slide

Work Energy Theorem

Question

A sphere of mass 2 kg is moving on a frictionless horizontal table with velocity v. It strike with a spring of constant 1 N/m and compresses it by 4 m. The velocity (v) of the sphere is :

Moderate

A

4 m/s
B

$2 \sqrt{2} m / s$
C

2 m/s
D

$\sqrt{2} m / s$

Solution

As per work energy theorem $w_{sp} = ΔK . E$
$\Rightarrow \frac{1}{2} {Kx}^{2} = \frac{1}{2} {mv}^{2}$
$\Rightarrow v = \sqrt{\frac{K}{m}} x$
$= \sqrt{\frac{1}{2}} . 4 = 2 \sqrt{2} m / s$

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