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The rotational kinetic energy of a solid...

The rotational kinetic energy of a solid sphere of mass 3 kg and radius 0.2 rolling down an inclined plane of height 7 m is

A

42 J

B

60 J

C

36 J

D

70 J

Text Solution

Verified by Experts

The correct Answer is:
B
From the law of conservation of energy,
initial potential energy = final rotational kinetic energy
`therefore " " "mgh" = (1)/(2) mv^(2) + (1)/(2) I omega^(2) = (1)/(2)mR^(2) omega^(2) + (1)/(2) ((2)/(5) mR^(2) ) omega^(2)`
= `(1)/(2) mR^(2) omega^(2) + (1)/(5) mR^(2) omega^(2) = (7)/(10) mR^(2) omega^(2)`
Rotational kinetic energy,
`(1)/(5) mR^(2) omega^(2) = (2)/(7) xx (7)/(10) mR^(2) omega^(2)`
= ` (2)/(7) mgh = (2)/(7) xx 3 xx 10 xx 7 = 60 J `
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