Question

An ice cube is kept on an inclined plane of angle $30{}^{\circ }$ . Coefficient of kinetic friction between block and incline plane is $\frac{1}{\sqrt{3}}.$ . What is acceleration of block?

• A. Zero
• B. $2m/s^2$
• C. $1.5m/s^2$
• D. $5m/s$

Answer 1

Answer: (A)

We can realise the situation as shown. Maximum retadation.
$a=\frac{f_k-mg\sin \theta }{m}$
$=\frac{{\mu }_{k}mg\cos \theta -mg\sin \theta }{m}$
$=\frac{\frac{1}{\sqrt{3}}mg\cos {30}^o-mg\sin {30}^o}{m}(\theta ={30}^o)$
$=\frac{\frac{1}{\sqrt{3}}g\times \frac{\sqrt{3}}{2}-g\times \frac{1}{2}}{1}$
$=0$
Hence, under the effect of kinetic friction between, block and inclined plane, acceleration of block is zero.