A smooth inclined plane of angle of inclination `30^(@)` is placed on the floor of a compartment of a train moving with a constant acceleration a. When a block is placed on the inclined plane, it does not slide down or up the plane. The acceleration a must be

Options

A. g
B. `(g)/(2)`
C. `(g)/sqrt(2)`
D. `(g)/sqrt(3)`

Answer

d

Explanation

When the train is accelerating in forward direction then reaction of this acceleration on block is in the backward direction
Then resolving `vecg` and `veca` into components
The block will stay at rest when a `cos theta = g sintheta`
`a=g tan theta`
`since theta = 30^(@) :. a=(g)/(sqrt3)` Hence correct choice is (d)