A cylinder of mass M and radius 2R has a groove of radius R. A block of mass m is hung from the circumference of the cylinder and the cylinder itself is hung from a rigid support by a thread wound on the groove as shown in the figure. If the acceleration of centre of mass of the cylinder is `'a_(1)'` , accelration of the block is `a_(2)` downward and angular acceleration of the cylinder is `alpha`, then relation between `a_(1) , a_(2)` and `alpha` will be

Options

A. `a_(1) - alpha R = a_(2)`
B. `a_(1) - 2alpha R = a_(2)`
C. `a_(1) + a_(2) = ( alpha R)/( 2)`
D. `a_(1) - a_(2) = 3alpha R `

Answer

B