A solid sphere of mass 2 kg and radius 1 m is free to rotate about an axis passing through its centre. Find a constant tangential force F requird to rotate the sphere I that tim interval.

A solid sphere of mass 2 kg and radius 1 m is free to rotate about an

1.	A solid sphere of mass 2 kg and radius 1 m is free to rotate about an axis passing through its centre. Find a constant tangential force F requird to rotate the sphere I that tim interval.
Answer» Solution :Since, the force is constant the torque produced by it and the angular ACCELERATION will be constant. HENCE, we can apply `omega=omega_(0)+alphatimplies10=0+(alpha)(2)impliesalpha=5rad//s^(2)` Further, the force is tangential. Therefore, the PERPENDICULAR distance from the axis of rotation will be equal to the radius of the sphere, `thereforealpha=(tau)/(I)=(F.R)/((2)/(5)mR^(2))=(5F)/(2mR)` or `F=(2mRalpha)/(5)` LTBR Substituting the value, we have `F=((2)(3)(1)(5))/((5))=4N` Further, angle rotated `theta=(1)/(2)alphat^(2)=(1)/(2)(5)(2)^(2)=10rad` `therefore` number of rotations `n=(theta)/(2pi)=(10)/(2pi)=(5)/(pi)`