Question

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

• A. $\frac{5}{2}\frac{gd}{R^2}$
• B. $\frac{5}{7}\frac{gd}{R^2}$
• C. $\frac{5}{2}\frac{d(g+{\omega }^{2}R)}{R^2}$
• D. $\frac{5}{7}\frac{d(g+{\omega }^{2}R)}{R^2}$

Answer 1

The correct option is D $\frac{5}{7}\frac{d(g+{\omega }^{2}R)}{R^2}$

Since, pure rolling

hence arc of point P is $m{w}^{2}R$

with respect to point P

$\tau p=I_p\alpha$

$\Rightarrow \left(mg+m{w}^{2}R\right)d=\frac{1}{5}m{R}^2.\alpha$

$\Rightarrow \alpha =\frac{5}{7}\frac{d\left(g+w^{2}R\right)}{R^2}$