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If a solid sphere of mass 1kg and radiu...

If a solid sphere of mass ` 1kg` and radius `0.1 m` rolls without slipping at a unifrom velocity of `1 ms^(-1)` along a stright line on a horizontal floor, the kinetic energy of the sphere is

A

`(2)/(5)J`

B

`1 J`

C

`(7)/(10) J`

D

`(7)/(5) J`

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `m = 1 kg, r = 0.1 m, v = 1 ms^(-1)`
`K.E.` of sphere `= (1)/(2)mv^(2) + (1)/(2)I omega^(2)`
As `I = (2)/(5)mr^(2) and omega = (v)/(r )`
`:. K.E.` of sphere
`= (1)/(2)mv^(2) + (1)/(2) xx (2)/(5)mr^(2) ((v)/(r ))^(2) = (7)/(10)mv^(2)`
`= (7)/(10) xx 1(1)^(2) = (7)/(10)J`
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