Q. 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 $B$ ?
AIEEEAIEEE 2010Laws of Motion
Solution:
$mg \,sin\,\theta = ma$
$\therefore \quad a = g \,sin\,\theta$
where a is along the inclined plane
$\therefore \quad$ vertical component of acceleration is $g \,sin^{2}\,\theta $
$\therefore \quad$ relative vertical acceleration of A with respect to B is
$g\left[sin^{2}\, 60- sin^{20}\, 30\right] = \frac{g}{2} = 4.9 \,m/ s^{2}$ in vertical direction.
