Question

Two fixed frictionless inclined plane making an angle ${30}^o$ and ${60}^o$ 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. $4.9m{s}^{-2}$ in horizontal direction
• B. $4.9m{s}^{-2}$ in vertical direction
• C. $9.8m{s}^{-2}$ in vertical direction
• D. zero

Answer 1

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

$mgsin\theta =ma$

$\therefore a=gsin\theta$
where a is along the inclined plane
$\therefore$ vertical component of acceleration is $g{\sin }^2\theta$
$\therefore$ Relative vertical acceleration of $A$ with respect to $B$ is

$g[{\sin }^{2}60-{\sin }^{2}30]=\frac{g}{2}=4.9m/s^2$ in vertical direction