A solid sphere slides down a smooth inclined plane of inclination `theta` with acceleration `a_(1)`. A disc rolls down a rough inclined plane of inclination `theta` with acceleration `a_(2)`. Value of `(a_(1))/(a_(2))` is

Options

A. `3/2`
B. `2/3`
C. `1/2`
D. 2

Answer

A

Explanation

Acceleration of solid sphere sliding down an inclined plane `a_(1)=g sin theta`
For disc plane is rough, so it will roll down the incline and its acceleration in rolling is given as
`a_(2)=(g sin theta)/(1+I/(MR^(2)))=(g sin theta)/(1+(((MR^(2))/2))/(MR^(2)))=(2g sin theta)/3`
`implies(a_(1))/(a_(2))=(g sin theta)/(((2gsin theta)/3))=3/2`