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A uniform solid spherical ball is rollin...

A uniform solid spherical ball is rolling down a smooth inclined plane form a height h. the velocity attained by the ball when it reaches the bottom of the inclined plane is v. If the ball is now thrwn vertically upwards with the same velocity v. the maximum height to which the ball will rise is

A

`(5h)/(8)`

B

`(3h)/(5)`

C

`(5h)/(7)`

D

`(7h)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
C
`I = (2)/(5)mr^(2),` where r = radius of the ball, m = mass of the ball
So, mgh` = (1)/(2) mv^(2) + (1)/(2) I omega^(2) " "or, v = sqrt((10gh)/(7))`
In case of upward motion of the ball,
` v^(2) = u^(2) - 2 gh. " " or, u^(2) = 2 gh. [ because v = 0 ]`
or, `(10 gh)/(7) = 2 gh. " "or, h. = (5h)/(7)`
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