Question

The two blocks A and B of equal mass are initially in contact when released from rest on the inclined plane. The coefficients of friction between the inclined plane A and B are ${\mu }_1$ and ${\mu }_2$ respectively. (Given $\theta$ is greater than any of the angle of repose of the blocks.)

• A. If ${\mu }_1>{\mu }_2$, the blocks will always remains in contact.
• B. If ${\mu }_1<{\mu }_2$, the blocks will slide down with different accelerations.
• C. If ${\mu }_1>{\mu }_2$, the blocks will have a common acceleration $\frac{1}{2}({\mu }_1+{\mu }_2)gsin\theta$.
• D. If ${\mu }_1<{\mu }_2$, the blocks will have a common acceleration $=\frac{{\mu }_1{\mu }_{2}g}{{\mu }_1+{\mu }_2}sin\theta$.

Answer 1

Answer: (A), (B)

The correct options are
A If ${\mu }_1>{\mu }_2$, the blocks will always remains in contact.
B If ${\mu }_1<{\mu }_2$, the blocks will slide down with different accelerations.

The block with lower value of $\mu$ tend to have greater acceleration down the slope. Hence, if ${\mu }_1>{\mu }_2$ the blocks will always remains in contact and if ${\mu }_1<{\mu }_2$ the blocks will slide down with different accelerations.