Question

Find out the distance travelled by the block as shown in figure. If the initial speed of the block is $V$ and $\mu$ is the friction coefficient between the surface of block and ground.

• A. $\frac{V^2}{2\mu g}$
• B. $\frac{V^2}{\mu g}$
• C. $\frac{V^2}{3\mu g}$
• D. $\frac{V^2}{5\mu g}$

Answer 1

The correct option is A $\frac{V^2}{2\mu g}$

Let the block moves $l$ distance before comes to rest.


Applying work- energy theorem, we get

$W_{allforces}=K{E}_f-K{E}_i$

Here, only friction force is doing work, so

$-\mu mgl=(0-\frac{1}{2}m{V}^2)$

$\mu gl=\frac{1}{2}{V}^2$

$\therefore l=\frac{V^2}{2\mu g}$

Hence, option $\left(a\right)$ is correct.