Question

Two fixed frictionless inclined planes making an angle ${30}^0$ and ${60}^0$ with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B

• A. 4.9 $m{s}^{-2}$ in vertical direction
• B. 4.9 $m{s}^{-2}$ in horizontal direction
• C. 9.8 $m{s}^{-2}$ in vertical direction
• D. Zero

Answer 1

The correct option is A 4.9 $m{s}^{-2}$ in vertical direction

acceleration along the inclined plane $=g\sin \theta$

Vertical component of acceleration is $=g{\sin }^2\theta$

therefore$,$ the relative vertical acceleration of $A$ with respect to $B$ is

$g\left[{\sin }^{2}60-{\sin }^{2}30\right]=\frac{g}{2}=4.9m/s^2$

in the vertical direction

Hence,

option $\left(A\right)$ is correct answer.