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  • Help me answer: - Motion of System Of Particles and Rigid Body - NEET

The ratio of the accelerations for a solid sphere (mass 'm' and radius 'R') rolling down an incline of angle ' \theta' Without slipping and slipping down the incline with rolling is:

  • Option 1)

    5 : 7

  • Option 2)

    2 : 3

  • Option 3)

    2 : 5

  • Option 4)

    7 : 5

 

Answers (1)

best_answer

As we learnt in

Rolling of a body on an inclined plane -

a= frac{gsin Theta }{1+frac{K^{2}}{R^{2}}}

f= frac{mgsin Theta }{1+frac{R^{2}}{K^{2}}}

- wherein

K=Radius of gyration

Theta = Angle of inclination

 

 

  

 

 

 

a=\frac{g\sin \Theta }{1+\frac{K^{2}}{R^{2}}}

For solid sphere  K^{2}=\frac{2}{5}R^{2}

                                =\frac{g \sin \Theta }{\frac{7}{5}}

a_{1}=\frac{5}{7}\:g\sin \Theta

\frac{a_{1}}{a_{2}}=\frac{\frac{5}{7}\:g\sin \Theta }{g\sin \Theta }

\frac{a_{1}}{a_{2}}=\frac{5}{7}


Option 1)

5 : 7

This is correct option

Option 2)

2 : 3

This is incorrect option

Option 3)

2 : 5

This is incorrect option

Option 4)

7 : 5

This is incorrect option

Posted by

prateek

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