Question

A block is placed on an inclined plane moving towards right horizontally with an acceleration $a_{0}=g$ . The length of the plane $AC=1 \, m$ . Friction is absent everywhere. The time taken by the block to reach from $C$ to $A$ is $\left(g = 10 \, m / s^{2}\right)$

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

Answer 1

Answer: (B)

Drawing a free body diagram of the block with respect to the plane.

Acceleration of the block up the plane is
$a=\frac{mgcos 30 ^\circ - mgsin ⁡ 30 ^\circ }{m}=\left(\frac{\sqrt{3} - 1}{2}\right)g=3.66 \, m/s^{2}$
Applying $s=\frac{1}{2}at^{2}$
$t=\sqrt{\frac{2 s}{a}}=\sqrt{\frac{2 \times 1}{3 .66}}=0.74 \, s$