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

Options

A. `sin^(-1){1-e^(2)(1-cos theta_(0))}`
B. `cos^(-1){1-e^(2)(1-cos theta_(0))}`
C. `Tan^(-1){1-e^(2)(1-cos theta_(0))}`
D. Zero

Answer

B

Explanation

Speed just before collision `=sqrt(2gl(1-cos_(0)^(.)))`
Speed just after collosion : `esqrt(2gl(1-cos_(0)^(.)))`
from conservation of energy,
`(1)/(2)me^(2)[2gl(1-cos_(0)^(.))]=mgl(1-cos^(.))`
`therefore^(.)=cos^(-1){1-e^(2)(1-cos_(0)^(.))}`