A solid cylinder of uniform density, mass m$1$ and radius r$1,$ can rotate freely

about a fixed horizontal axle along its central axis. A light string is wrapped

around both this cylinder and another similar cylinder of mass m$2$ and radius

r$2,$ see diagram below. This second cylinder falls under gravity, and hence also

rotates, unwinding the string from both cylinders. Assume the length of string

between the two cylinders remains vertical as shown. Find an expression for

the linear acceleration of the second cylinder and show that, for m$1=2$m$2,$ this

acceleration is $0\mathrm{.}75$ g$.$