A glass ball is shot to hit a wall from a point on a smooth floor. If the ball returns back to the point of projection in twice the time taken in reaching the wall, the coefficient of restitution between the glass ball and the wall is

ω rad/sec is the angular velocity of a crank whose radius is r. If it makes θ° with inner dead centre and obliquity of the connecting rod l is φ, the velocity v of the piston, is given by the equation