Question

A block of mass m= 0.1 kg is released from a height of 4m 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. $29m$
• B. $49m$
• C. $59m$
• D. $109m$

Answer 1

Answer: (C)

$59m$

We have the equation,

$mgh=\mu mgd$

Also,

$d=\frac{h}{\mu }=\frac{4}{0.1}=40m$

It is the total path on the rough surface,

$n=\frac{40}{2}=20$

So, it travels through $BC,20$ times. But the last time it cannot move from $B$ to $A$. Thus, it travels through $AB$

So,

$20-1=19times$

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

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