A smooth rod length `l` is kept inside a trolley at an angle `theta` as shown in the figure. What should be the acceleration `a` of the trolley so that the rod remain in equilibrium with respect to it?

Options

A. `g tan theta`
B. `g cos theta`
C. `g sin theta`
D. `g cot theta`

Answer

D

Explanation

`FBD` of rod w.r.t. trolley

`N_(1) = mg` …(i)
`N_(2) = mg` …(ii)
Net torque about point `C = 0`
`:. N_(1) = ((1)/(2) sin theta) = N_(2) = ((1)/(2) cos theta)`
or `(ma) (sin theta) = (mg) (cos theta)`
`rArr a = g cot theta`