Figure below shows a small mass connected to a string, which is attached to a vertical post. If the ball is released when the string is horizontal as shown, the magnitude of the total acceleration (including radial and tangential) of the mass as a function of the angle `Theta`is

Options

A. `g sin theta`
B. `gsqrt(3 cos^2 theta +1)`
C. `g cos theta`
D. `gsqrt(3 sin^2 theta +1)`

Answer

D

Explanation

Radial acceleration = `v^2/R = (2gl sin theta)/l = 2g sin theta`
`[ :. v = sqrt(2gh)]`
Tangential acceleration `= g cos theta`
Total acceleration
`=sqrt(4g^2 sin^2 theta cos^2 theta + g^2 cos^2 theta )implies g sqrt(1+3 sin ^2 theta)`