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A small sphere of mass 1 kg is rolling w...

A small sphere of mass 1 kg is rolling without slipping with linear speed
`v=sqrt((200)/(7) m//s`

It leaves the inclined plane at point C.
Find the linear speed at point C.

A

`sqrt(100/7) m//s`

B

`sqrt(50/7) m//s`

C

`sqrt(100/35) m//s`

D

`sqrt(200/35) m//s`

Text Solution

Verified by Experts

The correct Answer is:
A
In case of solid sphere, `K_(R)/K_(T) = 2/5`. If pure rolling `(v=Romega)` is taking place.
`therefore` Energy at bottom `E_(B) = 7/5 K_(T) = 7/5(1/2 mv^(2)) = 7/5 xx 1/2 xx (sqrt(200/7))^(2) = 20 J`
Kinetic energy at top `K_(C) = E_(B) - mgh = 20-(1) (10)(1) = 10J`
Again the ratio of `K_(R)/K_(T)` will be `2/5`
`therefore K_(T) = 5/7 xx 10 = 50/7 J` or `1/2 mv_(c)^(2) = 50/7 therefore v_( c) =sqrt(100/7) m//n` (as m=1 kg)
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