A pendulum of mass m and length l is suspended from the ceiling of a trolley which has a constant acceleration a in the maximum deflection `theta` of the pendulum from the vertical.

Explanation

The free-body diagram of the pendulum with respect to trolley is shown in figure

Free-body diagram of the pendulum bob with respect to trolley.
The forces acting on the bob are:
* the gravity, `mg`
* the pseudo force, `ma`
* the tension, `T`
The work done by gravity is `W_g=-mgl(1-costheta)`
`impliesW_g=-mgl(1-costheta)=-mgl(2sin^2theta/2)`
The work done by pseudo force, `W_(ps)=mal sin theta`
The work done by tension `W_T=0`
At the position of maximum deflection, the velocity of the bob is zero, `DeltaK=0`.
Applying work-energy theorem, we get
`W_g+W_(ps)+W_T=DeltaK`
`-mg[2sin^2theta/2]+ma[2sintheta/2costheta/2]=0`
`tantheta/2=a/g` or `theta=2tan^-1(a/g)`