Question

A block of mass $m$ is sliding on a fixed smooth inclined plane of angle $\theta = 30^{\circ}$ in case $(I)$. In case $(II)$ inclined plane is accelerated horizontally so that the block does not slide with respect to it. The ratio of acceleration of the block in horizontal direction in two cases is

• A. $\frac{3}{2}$
• B. $\frac{3}{4}$
• C. $\frac{1}{4}$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

In case $(I)$, acceleration of block in horizontal direction
$a_| = (g\,sin\,30^{\circ}) \,cos\,30^{\circ}\,\, ...(1)$
In case $(II)$, acceleration of block in horizontal direction is acceleration of wedge.
$a_{||} = g\,tan\,30^{\circ} ...(2)$
Ratio $(\frac{a_|}{a_{||}}) = cos^2 \,30^{\circ}$
$=\frac{3}{4}$