Question

Questions 7-9 A cylinder of mass M is free to slide on a frictionless horizontal shaft passing through its axis. A ball of mass m is attached to the cylinder by a massiess string of length . Initially, both the cylinder and the ball are at rest, with the d center of the cylinder at a perpendicular distance zo from the y-axis, and the ball displaced by an angle 8 /2 to the right relative to the vertical. Use the coordinate system indicated in the figure and assume that the motion takes place on the ry plane 8. If the ball is released from its initial position (zo +(,d) with zero initial velocity, what will be its coordiates (,) when it is at the bottom of its swing,i.e., when 6-0

Answer 1

Apply conservation of momentum in the x direction. The initial velocity of center of mass in the x direction is 0 and it continues to be 0 because of conservation of momentum. So, we can say that the x coordinate of the center of mass remains stationary.

$Mx_0+m(x_0+l)=Mx'+mx'$

$x'=x_0+\frac{ml}{M+m}$

correct answer (b)