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An iron ball of mass m, suspended by a l...

An iron ball of mass `m`, suspended by a light inextensible string of length `l` from a fixed point `O`, is shifted by `theta_(0)` as shown so as to strike the vertical wail perpendicularly.The maximum angle made by the string with vertical after the first collision, if `e` is the coefficient of restitution, is

A

`sin^(-1){1-e^(2)(1-costheta_(0))}`

B

`cos^(-1){1-e^(2)(1-costheta_(0))}`

C

`tan^(-1){1-e^(2)(1-costheta_(0))}`

D

zero

Text Solution

Verified by Experts

Speed just before collision `=sqrt(2gl(1-costheta_(0)))`
Speed just after collision`=esqrt(2gl(1-costheta_(0)))`
From `COE`,
`(1)/(2)me^(2)[2gl(1-costheta_(0))]=mgl(1-costheta)`
`:. theta=cos^(-1){1-e^(2)(1-costheta_(0))}`
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