A bob of mass `m` attached with a string of length `l` tied to a point on ceiling is released from a position when its string is horizontal. At the bottom most point of its motion, an identical mass `m` gently stuck to it. Find the maximum angle from the vertical to which it rotates.

Options

A. (a) `cos^-1(2/3)`
B. (b) `cos^-1(3/4)`
C. (c) `cos^-1(1/4)`
D. (d) `60^@`

Answer

B

Explanation

`v_m=sqrt(2gl)`
From conservation of linear momentum,
`v_(2m)=(v_m)/(2)=(sqrt(2gl))/(2)`
Now, `h=(v_(2m))/(2g)=l/4`
But `h=l(1-cos theta)`
`:. l/4=l(1-costheta)`
`:. theta=cos^-1(3/4)`