A tangential force F acts at the top of a thin spherical shell of mass m and radius R . The acceleration of the shell if it rolls without slipping is

Step-by-step solution

Torque due to the force F on a thin spherical shell, aligned & =r F & =2 R F 90^ =2 R F [ 90^ =1 ] aligned Where, I is moment of inertia of a thin spherical shell. From parallel axes's theorem, moment of inertia of spherical shell, I=I_ cm +M r^2 or I= 2 3 M R^2+M R^2 ( r=R) From Eqs. (i), we get gathered = 2 R F 2 3 M R^2+M R^2 = ( 6 5 ) F R M gathered Hence, the tangential acceleration, a_T=R or a_T= ( 6 5 ) F R M R= 6 5 F M