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A small sphere D of mass and radius rols...

A small sphere `D` of mass and radius rols without slipping inside a large fixed hemispherical radius `R( gt gt r)` as shown in figure. If the sphere starts from rest at the top point of the hemisphere normal force exerted by the small sphere on the hemisphere when its is at the bottom `B` of the hemisphere.
.

A

`(10)/(7) mg`

B

`(17)/(7) mg`

C

`(5)/(7) mg`

D

`(7)/(5) mg`

Text Solution

Verified by Experts

The correct Answer is:
B
From energy conservation gain of `K.E = loss of P.E`
`(1)/(2) mv^(2) (1 +(K^(2))/(R^(2))) = mgR rArr (1)/(2) mv^(2) (1 +(2)/(5)) = mgR`
` = sqrt((10)/(7) gR)`
For circular motion at bottom
`N - mg = (mv^(2))/( R) rArr N = mg + (m)/( R) xx (10)/(7) gR`
`N = (17)/(7) mg`.
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