A solid sphere is rolling on a rough surface, whose centre of mass is at `C` at a certain instant. Find at that instant it has angular velocity `omega`. Its radius is `R`. Find the angular acceleration at that instant mass of sphere is `m`

Options

A. `(5)/(2)(gd)/(R^(2))`
B. `(5)/(7)(gd)/(R^(2))`
C. `(5)/(2)(d(g+omega^(2)R))/(R^(2))`
D. `(5)/(7)(d(g+omega^(2)R))/(R^(2))`

Explanation

[`momega^(2)R` is pseudo force]
If we will take torque about `P` then we have to apply pseudo force `momega^(2)R` on centre of mass because this axis has
Acceleration `=omega^(2)R` towards `0`.
Then `T_(P)alpha=(mg+momega^(2)R)d`
`alpha(5)/(7)(d(g+omega^(2)R))/(R^(2))`