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Confused! kindly explain, - 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 and incline of angle '\theta' without slipping and slipping down the incline without rolling is

  • Option 1)

    5:7

  • Option 2)

    2:3

  • Option 3)

    2:5

  • Option 4)

    7:5

 
Answers (1)
110 Views

As discussed 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_{1}=\frac{g \sin \Theta}{1+\frac{K^{2}}{R^{2}}}\: (Rolling)

a_{2}=g \sin \Theta\: (Slipping)

\therefore \frac{a_{1}}{a_{2}}=\frac{1}{1+\frac{K^{2}}{R^{2}}}=\frac{1}{1+\frac{2}{5}}=\frac{5}{7}=5:7 


Option 1)

5:7

This option is correct.

Option 2)

2:3

This option is incorrect.

Option 3)

2:5

This option is incorrect.

Option 4)

7:5

This option is incorrect.

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