Question

A block of mass m = 0.1 kg is released from a height of 4 m on a curved smooth surface. On the horizontal surface, path AB is smooth and path BC offers coefficient of friction $\mu =0.1$. If the impact of block with the vertical wall at C be perfectly elastic, the total distance covered by the block on the horizontal surface before coming to rest will be : (take $g=10m/s^2$)

• A. 29 m
• B. 49 m
• C. 59 m
• D. 109 m

Answer 1

The correct option is C 59 m

Given:

Mass $=0.1kg$

Height $=4m$

Length of the path $AB=1cm$

Length of the path $BC=2cm$

Impact at $C$ is perfectly elastic

The total distance covered by the block on the horizontal surface before coming to rest can be given by,

We have,

$mgh=\mu mgd$

$d=\frac{h}{\mu }=\frac{4}{0.1}$

$d=40m$

Number of times, $n=\frac{40}{2}=20times$.

$BC=20times$

$AB=19times$

Distance $=20\left(2\right)+19\left(1\right)=59m$

Hence, the distance is $59m$.