Question

A block is placed on an inclined plane moving towards right horizontally with an acceleration $a_0=g$. The length of the plane $AC$ = $1\text{m}$. Friction is absent everywhere. The time taken by the block to reach from $C$ to $A$ is approximately $(g=10{\text{m/s}}^2)$

• A. $1.2$ $s$
• B. $0.74s$
• C. $2.56s$
• D. $0.42s$

Answer 1

The correct option is B $0.74s$

Drawing free body diagram of block with resepct to plane.

Acceleration of the block up the plane is
$a=\frac{\text{mg cos}{30}^{\circ }-\text{mg sin}{30}^{\circ }}{m}$

$=\left(\frac{\sqrt{3}-1}{2}\right)g=3.66{\text{m/s}}^2$
On applying, $s=\frac{1}{2}a{t}^2$
$t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2\times 1}{3.66}}=0.74s$