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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

 
Answers (1)
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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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