Question

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

Answer 1

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))}`