Figure shows a mass m placed on a frictionless horizontal table and attached toa string passing through a mall hole in the surface. Initially, themas movesin a circle of radius `r_0` with a speed `v_0` and the ree end of the string is held by a person. The person pulls on the string slowly to decrease the radius of th circle of r. a. Find the tension in the string when the mass moves in the circle of radius r. b. Calculate the chasnge in the kinetic energy of the mass

Explanation

The torque acting on the mass m about the vertical axis through the hole is zero. The angular momentum about this axis, therefore, remains constant. If the speed of the mass is v whenit moves in the circel of radius r we have
`mv_0r_0=mvr`
or `v=r_0/rv_0`.......i ltbr. a. the tension `T=(mv^2)/r=(mr_0^2v_0^2)/r^3
b. The change in kinetic energy `=1/2mv^2-1/2mv_0^2`
Byi it is `=1/2mv_0^2[r_0^2/r^2-1]`