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# Try this! A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy(Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy
(Kr) simultaneously. The ratio Kt : (Kt + Kr) for the sphere is

• Option 1)

10 : 7

• Option 2)

5 : 7

• Option 3)

7 : 10

• Option 4)

2 : 5

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As we have learned

Kinetic energy of a body in combined rotation and translation -

$K.E=\frac{1}{2}\, I_{cm}w^{2}+\frac{1}{2}mv_{0}\, ^{2}$

- wherein

$\frac{1}{2}mv_{0}\, ^{2}$ =  Translational kinetic energy of centre of mass

$\frac{1}{2}\, I_{cm}w^{2}$  =  Rotational kinetic energy about centre of mass

$k_{t}=1/2mv_{c}m^{2}$

$k_{r}=1/2 Iw^{2}= 1/2 (2/5 mr^{2})(v/r)^{2}=1/5mv^{2}$

$\frac{k_{t}}{kt+k_{r}}= \frac{\frac{1}{2}mV_{c}m^{2}}{(\frac{1}{2}+\frac{1}{5})mv^{2}}=5/7$

Option 1)

10 : 7

This is incorrect

Option 2)

5 : 7

This is correct

Option 3)

7 : 10

This is incorrect

Option 4)

2 : 5

This is incorrect

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