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a solid, a ring and a circular disc of identical radii are rolling down on a inclined plane without slipping from the height starting from rest. which will reach the bottom first and which ill reach the bottom least

a solid, a ring and a circular disc of identical radii are rolling down on a inclined plane without slipping from the height starting from rest. which will reach the bottom first and which ill reach the bottom least

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Student
 
 

                                                     solid sphere              disc              solid cylinder

 

Moment of Inertia (I)                    (2/5)MR2                  MR2 /2             MR2 /2

 

Radious of Gyration (K)                Underoot(2/5)      R/root2           R/root2

 

 

 

Any of them on rolling on inclined plane will have an acceleration,

 

a = gsin8/R2 + K2

 

It means maximum radius of gyration having object will have minimum acceleration.

 

Decrease in acceleration .i.e decrease in velocity and thus kinetic energy.

 

 

 

Now, Solid sphere has lowest value of ''K'' thus it rolls down with maximum speed.

 

Hence it will reach the bottom first.

 

And disc and solid sphere will reach at the same time with same speed.

 
Regards
Arun (askIITians forum expert)

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