First slide

Work Energy Theorem

Question

A block rests on a rough horizontal surface. It is projected along the surface. The block comes to rest after travelling distance 5m. If the mass of the block is halved and velocity is doubled, the distance covered by the block before it comes to rest is,

Moderate

A

10 m
B

20 m
C

30 m
D

40 m

Solution

By work - energy principles,
$\begin{array}{l} 0 - \frac{1}{2} {mV}^{2} = - (μmg) S \Rightarrow S = \frac{V^{2}}{2 μg} \Rightarrow S \propto V^{2} \\ ∴ \frac{S^{1}}{5} = {(\frac{2 V}{V})}^{2} \Rightarrow S^{1} = 20 m \end{array}$

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