Question

Two fixed frictionless inclined plane making an angle $30^{\circ }$ and $60^{\circ }$ with the vertical are shown in the figure. Two block $A$ 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. $9.8m{s}^{-2}$ in vertical direction
• C. zero
• D. $4.9m{s}^{-2}$ in vertical direction

Answer 1

Answer: (D)

$mgsin\theta =ma$
$\therefore a=gsin\theta$
where a is along the inclined plane
$\therefore$ vertical component of acceleration is $gsi{n}^2\theta$
$\therefore$ relative vertical acceleration of A with respect to B is
$g\left[si{n}^{2}60-si{n}^{20}30\right]=\frac{g}{2}=4.9m/s^2$ in vertical direction.