Question

In the case of different rolling bodies match the ratio of rotational kinetic energy to the total kinetic energy

List - I	List - II
a) hollow sphere	e) $2:5$
b) solid cylinder	f) $1:2$
c) solid sphere	g) $1:3$
d) hollow cylinder	h) $2:7$

• A. $a-h;b-g;c-e;d-f$
• B. $a-h;b-g;c-f;d-e$
• C. $a-e;b-g;c-h;d-f$
• D. $a-e;b-g;c-f;d-h$

Answer 1

The correct option is C $a-e;b-g;c-h;d-f$

$\frac{K_R}{K_R+K_T}=\frac{I(\frac{V}{R}{)}^2}{I(\frac{V}{R}{)}^2+V^2}=\frac{\left(\frac{I}{R^2}\right)}{\left(\frac{I}{R^2}\right)+1}$
for hollow sphere $=\frac{\frac{2}{3}}{\frac{2}{3}+1}=\frac{2}{5}$
Solid Cylinder $=\frac{\frac{1}{2}}{\frac{1}{2}+1}=\frac{1}{3}$
Solid Sphere $=\frac{\frac{2}{5}}{\frac{2}{5}+1}=\frac{2}{7}$
hollow Cylinder $=\frac{1}{1+1}=\frac{1}{2}.$