Question

Two fixed frictionless inclined planes making an angle $30^{\circ}$ and $60^{\circ}$ 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. $4.9 ms ^{-2}$ in vertical direction
• B. $4.9 ms ^{-2}$ in horizontal direction
• C. $9.8 ms ^{-2}$ in vertical direction
• D. Zero

Answer 1

Answer: (A)

Relative vertical acceleration of A with respect to B
$=g\left(\sin ^{2} 60^{\circ}-\sin ^{2} 30^{\circ}\right)$
$=9.8\left(\frac{3}{4}-\frac{1}{4}\right)=4.9 m / s ^{2}$