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 by the horizontal component of tension T.
`Tsintheta=ma" . . . . .(i)"`
`T=costheta=mg" . . .. .(ii)"`
From equation (i) and (ii)
`tan theta=1/grArrtheta=tan^(-1)((a)/(g))`
In a non-inertial frame


Fig. 1.25
Figure represents free Body diagram of bob w.r.t car. In the non-intertial frame of the car, the bob is in static equilibrium under the action of three froces, T, mg and ma (pseudo force)
`Tsintheta=ma" . . . . (iii)"`
`Tcostheta=mg" . . . . .(iv)"`
`tantheta=1/g" "rArr" "theta=tan^(-1)((a)/(g))`