Question

The moments of inertia of two rotating bodies A and B are IA and IB (IA > IB). If their angular momenta are equal, then

• A. Kinetic energy of A = Kinetic energy of B
• B. Kinetic energy of A > Kinetic energy of B
• C. Kinetic energy of A < Kinetic energy of B
• D. Kinetic energy of the two bodies cannot be compared with the given data

Answer 1

Answer: (C)

Kinetic energy of A < Kinetic energy of B

Answer 2

(Given)

$\therefore \frac { \omega _ { \mathrm { A } } } { \omega _ { \mathrm { B } } } = \frac { \mathrm { I } _ { \mathrm { B } } } { \mathrm { I } _ { \mathrm { A } } }$ …(i)

Kinetic energy, $= \frac { 1 } { 2 } \mathrm { I } \omega ^ { 2 }$

$\therefore \frac { ( K . E ) _ { A } } { ( K . E ) _ { B } } = \frac { \frac { 1 } { 2 } I _ { A } \omega _ { A } ^ { 2 } } { \frac { 1 } { 2 } I _ { B } \omega _ { B } ^ { 2 } }$

(Using(i))

$= \frac { \mathrm { I } _ { \mathrm { B } } } { \mathrm { I } _ { \mathrm { A } } }$

As $\mathrm { I } _ { \mathrm { A } } > \mathrm { I } _ { \mathrm { B } }$ (Given)