Question

A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is –

• A. 2/5
• B. 2/7
• C. 3/5
• D. 3/7

Answer 1

Answer: (B)

2/7

Answer 2

Total energy

K = K_R + K_T = $\frac { 1 } { 2 }$ Iw² + $\frac { 1 } { 2 }$mv²

= $\frac { 1 } { 2 }$ w² + $\frac { 1 } { 2 }$ mr²w²

= $\frac { 1 } { 5 }$mr²w² + $\frac { 1 } { 2 }$ mr² w² = $\frac { 7 } { 10 }$ mr²w²

Now, rotational kinetic energy

K_R = $\frac { 1 } { 2 }$Iw² = $\frac { 1 } { 5 }$ mr²w²

\ $\frac { K _ { R } } { K }$ = = $\frac { 2 } { 7 }$