Question

Two discs rotating about their respective axis of rotation with angular speed 2 rad $s^{-1}$. and 5 rad $s^{-1}$ are brought into contact such that their axes of rotation coincide. Now, the angular speed of the system becomes. 4 rad $s^{-1}$. If the moment of inertia of the second disc is $1\times {10}^{-3}kg{m}^2$, then the moment of inertia of the first disc (in kg $m^2$) is

• A. $0.25\times {10}^{-3}$
• B. $1.5\times {10}^{-3}$
• C. $1.25\times {10}^{-3}$
• D. $0.75\times {10}^{-3}$
• E. $0.5\times {10}^{-3}$

Answer 1

The correct option is E $0.5\times {10}^{-3}$

Relation between war momentum and moment of inertia
$U+I\omega$
where $I_1=?$
$I_2=1\times {10}^{-3}kg-m^2$
${\omega }_1=2rad/s$
${\omega }_2=5rad/s$
$\omega =4rad/s$
So, $J=J_1+J_2$
$(I_1+1\times {10}^{-3})\times 4=I_1\times 2+5\times 1\times {10}^{-3}$
$4I_1+4\times {10}^{-3}=2I_1+5\times {10}^{-3}$
$2I_1=1\times {10}^{-3}$
$I_1=\frac{1}{2}\times {10}^{-3}$
$=0.5\times {10}^{-3}kg-m^2$