Question

A circular disc of mass $3kg$ is rotating freely in horizontal plane about vertical axis passing through its centre at the rate of $2.4rotation/sec$. Two bodies each of mass $0.5kg$ are gently attached to the rim of disc due to which its radius of gyration is increased by $20\%$, then its angular velocity is:

• A. $60rpm$
• B. $75rpm$
• C. $90rpm$
• D. $105rpm$

Answer 1

Answer: (B)

$75rpm$

Two bodies output $I_1=\frac{3R^2}{2}$
Radius of gyration $=$ k is increased by $20$.
$k_1=\sqrt{\frac{1}{2}}R$
$k_2=\frac{1.2}{\sqrt{2}}R,new{I}_2=4\times {\left(\frac{1.2R}{\sqrt{2}}\right)}^2$
Angular momentum is conserved.
$I_1{W}_2=I_2{w}_2$
$\frac{3R^2}{2}\times 2.4=4\times {\left(\frac{1.2}{\sqrt{2}}\right)}^2{R}^2{w}_2$
$w_2=1.2rps$
$w_2=1.2\times 60rpm.$
$=75rpm$