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A disc and a solid sphere of same radius...

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

A

solid sphere

B

both reach at the same time

C

depends on their masses

D

disc

Text Solution

Verified by Experts

The correct Answer is:
A
The acceleration of an object rolling down an inclined plane is given by
`a = (g sin theta)/(1 + I//mr^(2))`
For disc, `I = (1)/(2)mr^(2)`
`:. (I)/(mr^(2)) = (1)/(2), a = (2)/(3)g sin theta = 0.67 g sin theta`
For solid sphere,`I = (2)/(5)mr^(2)`
`:. (I)/(mr^(2)) = (2)/(5), a = (5)/(7) g sin theta = 0.71g sin theta`
Clearly, `a_("solid sphere") gt a_("disc") :. t_("solid sphere") lt t_("disc")`
Hence solid sphere gets to the bottom of the plane first.
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