Question

Three mass particle $A,B$ and $C$ having masses $m,2m$ and $3m$ respectively are rigidly attached to a ring of mass $m$ and radius $R$ which rolls on a horizontal surface without slipping. At a certain instant the velocity of the centre of the ring is $v_0$ as shown in the figure. the kinetic energy of the system is

• A. $7m{v}_0^2$
• B. $9m{v}_0^2$
• C. $m{v}_0^2$
• D. $\frac{7}{2}m{v}_0^2$

Answer 1

The correct option is B $9m{v}_0^2$

R.E.F image

$V_C=V_0+\sqrt{2}\leftarrow \sqrt{[N_0^2+V_0^2]}$

$V_B=V_0+V_0=2V_0$

$V_A=\sqrt{2}{V}_0$

$(Ke{)}_{nr}+K{E}_A+K{E}_B+K{E}_C=\frac{1}{2}m(\sqrt{2}{V}_0{)}^2+\frac{1}{2}2m\times \left(2V_0^2\right)$

$\frac{1}{2}\times m{V}_0^2+\frac{1}{2}3m\left(\sqrt{2}{V}_0^2\right)$

$\therefore (KE{)}_{Total}=9m{V}_0^2$ Ans.