Two fixed frictionless inclined plane making angles `30^(@)` and `60^(@)` 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 ?

Options

A. (a) `4.9 ms^-2` in horizontal direction
B. (b) `9.8ms^2` in vertical direction
C. (c) Zero
D. (d) `4.9ms^-2` in vertical direction

Answer

D

Explanation

`mg sin theta=ma` `:.` `a=g sin theta`
where a is along the inclined plane
`:.` vertical component of acceleration is `g sin^2 theta`
relative vertical acceleration of A with respect to B is
`g(sin^(2)60-sin^(2)30]=g/2=4.9 m//s^2` in vertical direction.