Question

A block weighing $10N$ travels down a smooth curved track $AB$ joined to a rough horizontal surface (see figure). The rough surface has a friction coefficient of $0.20$ with the block. If the block starts slipping on the track from a point $1.0m$ above the horizontal surface, then it would move a distance $s$ on the rough surface. The value of $s$ is $\left[g=10m{s}^{-2}\right]$

• A. 1 m
• B. 2 m
• C. 3 m
• D. 5 m

Answer 1

Answer: (D)

In the $AB$ path, Loss in $PE=$ Gain in $KE$
$mgh=\frac{1}{2}m{u}^2\Rightarrow u=\sqrt{2gh}=\sqrt{2\times 10\times 1}\times 2\sqrt{5}m/s$
On the frictional path, $W_{\text{friction }}=\Delta K$ $-\mu mg\cdot s=0-\frac{1}{2}m{u}^2\Rightarrow s=\frac{u^2}{2\mu g}$
$=\frac{4\times 5}{2\times 0.2\times 10}=5m$