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6.System of Particles and Rotational Motion
normal
$A$ ring of mass $m$ and radius $R$ has three particles attached to the ring as shown in the figure. The centre of the ring has a speed $v_0$. The kinetic energy of the system is: (Slipping is absent)
A
$6\, mv_0^2$
B
$12\,mv_0^2$
C
$12\,mv_0^2$
D
$8\,mv_0^2$
Solution
About instantaneous axis of rotation rolling system can be considered as pure rotation
$K E=\frac{1}{2} I \omega^{2}$$…(1)$
here $I=$ moment of inertia about instantaneous axis of rotation
$I=2 m(\sqrt{2} R)^{2}+m(2 R)^{2}+m(\sqrt{2} R)^{2}+I_{r \in g}$
$I=2 m(\sqrt{2} R)^{2}+m(2 R)^{2}+m(\sqrt{2} R)^{2}+m R^{2}$
$I=12 m R^{2}$
putting the value of $I$ in equation $(1)$
$K E=6 m R^{2} \omega^{2}$
$K E=6 m(R \omega)^{2}$
$K E=6 m v_{o}^{2}$
Standard 11
Physics
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