Question

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

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

Answer 1

The correct option is B $2m/s^2$

Ice cube is kept on inclined plane of angle ${30}^{\circ }$and kinetic friction is $\frac{1}{\sqrt{3}}$.

Now balancing forces

$mg\sin 30-{\mu }_{k}mg=ma$

$g\sin 30-{\mu }_{k}g=a$

$a=\left(\sin 30-{\mu }_k\right)g$

$a=\left(\frac{1}{2}-\frac{1}{\sqrt{3}}\right)g$

$a=\left(\frac{\sqrt{3}-1}{2\sqrt{3}}\right)g$

$a=0.2113\times 9.8$

$a=2.07m/s^2$

$a\approx 2m/s^2$

Thus acceleration of the block is $2m/s^2$.