Question

In the following figure, a body of mass 'm' is tied at one end of a light string and this string is wrapped around the solid cylinder of mass 'M' and radius 'R'. At the moment, t = 0 the system starts moving. If the friction is negligible, angular velocity at time, t would be

• A. $\frac{mgRt}{(M+m)}$
• B. $\frac{2Mgt}{R(M+2m)}$
• C. $\frac{2mgt}{R(M-2m)}$
• D. $\frac{2mgt}{R(M+2m)}$

Answer 1

The correct option is D $\frac{2mgt}{R(M+2m)}$

We know the tangential acceleration $a=\frac{g}{1+\frac{I}{m{R}^2}}=\frac{g}{1+\frac{1/2M{R}^2}{m{R}^2}}=\frac{2mg}{2m+M}$ $[AsI=\frac{1}{2}M{R}^{2}forcylinder]$
After time t, linear velocity of mass $m,v=u+at=0+\frac{2mgt}{2m+M}$
So angular velocity of the cylinder $\omega =\frac{v}{R}=\frac{2mgt}{R(M+2m)}.$