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A uniform solid sphere rolls on a horizo...

A uniform solid sphere rolls on a horizontal surface at 20 m/s. It, then, rolls up a plane inclined at `

A

16 m

B

20 m

C

28 m

D

36 m

Text Solution

Verified by Experts

The correct Answer is:
C
For the sphere, `K_("Translational")+K_("Rotational")=P.E.`
`(1)/(2)mv^(2)+(1)/(2)I omega^(2)=mgh`
`(1)/(2)mv^(2)+(1)/(2)((2)/(5)mR^(2))(v^(2))/(R^(2))=mgh " " [omega = (v)/(R )]`
`(1)/(2)mv^(2)+(1)/(5)mv^(2)=mgh`
`therefore (7)/(10)mv^(2)=mgh`
`therefore h = (7v^(2))/(10 g)=(7xx20xx20)/(10xx10)=28 m`
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