Figure shows a pendulum suspended from the roof of a car that has a constant acceleration a relative to the ground. Find the deflection of the pendulum from the vertical as observed from the ground frame and from the frame attached with the car.

Explanation

Figure represents free Body diagram of the bob w.r.t ground.
In an inertial frame the suspended bob has an acceleration a caused bythe horizontal component of tension T.
`T =sin theta = ma `….(i)
`T cos theta =mg ` ....(ii)
From equation (i) and (ii)
`tan theta = ( a)/( g) rArr q = tan^(-1)((a)/( g))`
In a non -inertial frame

Figure represents free Body diagram of bob w.r.t. car.
In a non-inertial frame of the car,the bob is in static equilibrium under the action of three forces, T , mg and ms( pseudo force )
`T sin theta = ma ` ....(iii)
`T cos theta = mg ` ....(iv)
From equation (iii) and (iv)
`tan theta = ( a)/( g) rArr theta = tan^(-1) ((a)/( g))`