Physics - Rotation Question with Solution | TestHub

$\text{a}=\frac{\text{g sin }\theta }{\left(1+\text{I/}{\text{mR}}^2\right)}$

${\text{a}}_{\text{S}}=\frac{\text{g sin }{\theta }_{\text{s}}}{\left(1+2/5\right)}$

${\text{a}}_{\text{C}}=\frac{g\; sin{\theta }_{\text{C}}}{\left(1+1/2\right)}$

Now, a_S= a_C

$\frac{g\; sin{\theta }_{\text{S}}}{\left(\frac{7}{5}\right)}=\frac{g\; sin{\theta }_{\text{C}}}{\left(\frac{3}{2}\right)}$

$\frac{5}{7}\text{ sin }{\theta }_{\text{S}}=\frac{2}{3}\text{ sin }{\theta }_{\text{C}}$

$\therefore \frac{sin{\theta }_{\text{C}}}{sin{\theta }_{\text{S}}}=\frac{5\times 3}{7\times 2}=\frac{15}{14}$