The given figure shows a small mass connected to a string which is atteched to a string , which is attached to a vertical post. If the mass is released from rest when the string is horizontal as shown the magnitude of the total acceleration of the mass as friction of the angle `theta` is

Options

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

Answer

C

Explanation

From conservation of energy `DeltaK + Delta U = 0`
`mgh = (1)/(2) mv^(2) mgl sin theta = (1)/(2) mv^(2)`
`implies a_(C) = 2g sin theta = (v^(2))/(l)` = radius acceleration
`g cos theta = a_(t)` = tangential acceleration

Total acceleration
`a = sqrt(a_( c)^(2) + a_(t)^(2)) = g sqrt(cos^(2) theta + (2 sin theta)^(2))`
`= g sqrt((1 - sin^(2) theta) + 4 sin^(2) theta) = g sqrt(1 + 3 sin^(2) theta)`.