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thick walled hollow sphere of radius R rolls down an incline...final vel at botm wen it rolls widout slipng is v..with slippng is 5v/4.wt is radius of gyratn?

thick walled hollow sphere of radius R rolls down an incline...final vel at botm wen it rolls widout slipng is v..with slippng is 5v/4.wt is radius of gyratn?

Grade:12

1 Answers

Nirmal Singh.
askIITians Faculty 44 Points
10 years ago
For radius of gyration -
Iaxis = mk^2
where k is the radius of gyration
so radius of gyration k = sqrt (Iaxis / m)
Iaxis about the rolling contact axis is Iy
So Iz = Ix +Iy
2/3mR^2 = 2Iy
Iy = 2/6mR^2 = Iaxis
so k = sqrt (2/6mR^2 / m)
k = sqrt(2/6R^2)
Regards,
Nirmal Singh
Askiitians faculty

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