A disk and a sphere o same radius but different masses roll off on two inclined planes of the same altitude and lengths. Which one of the two objects gets to the bottom of the plane first?

  • Option 1)

    Disk

  • Option 2)

    Sphere

  • Option 3)

    Both reach at the same time

  • Option 4)

    Depends on their masses

 

Answers (1)

As 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

 

 

V \alpha \frac{1}{\sqrt{1 + \frac{K^{2}}{R^{2}}}} \:\:,a\:\alpha \frac{1}{1 + \frac{K^{2}}{R^{2}}}

                               t\:\alpha \:\sqrt{1+ \frac{K^{2}}{R^{2}}}

If the value of  \frac{K^{2}}{R^{2}} is less, the moment of inertia will be less and greater will be its velocity. The solid body will reach the bottom first.


Option 1)

Disk

This answer is incorrect

Option 2)

Sphere

This answer is correct

Option 3)

Both reach at the same time

This answer is incorrect

Option 4)

Depends on their masses

This answer is incorrect

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