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Question: The total kinetic energy of rolling solid sphere having translational velocity v is:...

The total kinetic energy of rolling solid sphere having translational velocity v is:

A

7/10 mv2

B

1/2 mv2

C

2/5 mv2

D

10/7 mv2.

Answer

7/10 mv2

Explanation

Solution

KN=12mv2(1+K2R2)=12mv2(1+25)=710mv2\mathrm { K } _ { \mathrm { N } } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 } \left( 1 + \frac { \mathrm { K } ^ { 2 } } { \mathrm { R } ^ { 2 } } \right) = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 } \left( 1 + \frac { 2 } { 5 } \right) = \frac { 7 } { 10 } \mathrm { mv } ^ { 2 }