Question

Inside a railway bogie on a horizontal straight track, there is a smooth inclined plane of inclination '$\theta$' as shown in figure. A small block is kept on the inclined surface. If the block is to remain stationary on the inclined surface, the acceleration to be given to the bogie is:

• A. $gsin\theta$
• B. $gtan\theta$
• C. $g/tan\theta$
• D. $gcos\theta$

Answer 1

Answer: (B)

$gtan\theta$

Using pseudo force concept considering frame of accelerated bogie:
For the block to remain at one place forces along x - direction should balance.
$\Rightarrow macos\theta =mgsin\theta$
$\Rightarrow a=gtan\theta$