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. $4.9\, ms^{-2}$ in horizontal direction
• B. $9.8\, ms^{-2}$ in vertical direction
• C. zero
• D. $4.9\, ms^{-2}$ in vertical direction

Answer 1

Answer: (D)

$4.9\, ms^{-2}$ in vertical direction

Answer 2

$mg \,sin\,\theta = ma$ $\therefore\quad a = g \,sin\,\theta$ 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.