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

A bob of mass `m` attached with a string of length `l` tied to a point

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

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