Question

A uniform circular disc of radius $R$ is placed on a smooth horizontal surface with its plane horizontal and hinged al circumference through point $O$ as shown. An impulse $P$ is applied at a perpendicular distance h from its centre $C$. The value of $h$ so that the impulse due to hinge is zero, is

• A. $R$
• B. $R/2$
• C. $R/3$
• D. $R/4$

Answer 1

Answer: (B)

$R/2$

$\omega =\frac{Angularimpulse}{I}$ (about O)
$=\frac{P(R+h)}{\frac{3}{2}m{R}^2}$
Now, $v_{COM}=R\omega =\frac{PR(R+h)}{\frac{3}{2}m{R}^2}$
$P+P_{Hinge}=m{v}_{COM}=\frac{mpR(R+h)}{\frac{3}{2}m{R}^2}$
solving this equation, we get $h=\frac{R}{2}$