The total energy of a solid sphere of mass 300 g which rolls without slipping with a constant velocity of `5 ms^(-1)` along a straight line is

Options

A. `5.25 J`
B. `3.25 J`
C. `0.25 J`
D. `1.25 J`

Answer

A

Explanation

The kinetic energy `K = 1/2 I omega ^(2)`
For solid sphere `I _(CM) = (2)/(5) mr ^(2)`
`K R _("total ") = (1)/(2) ((2 )/(5) mr ^(2)) omega ^(2) +(1)/(2) mr ^(2) omega ^(2)`
` = 1/5 mr ^(2) omega ^(2) + 1/2 mr ^(2) omega ^(2)`
`= (7)/(10) mr ^(2) omega ^(2) " "(because v = r omega)`
`K E _("total") = (7)/(10 ) mv ^(2) =(7)/(10) xx (300)/(1000) xx 5 ^(2)`
`= 0.7 xx 0.3 xx 25 = 5.25J`