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A solid sphere and a solid cylinder are ...

A solid sphere and a solid cylinder are in pure roling on a rough curved surface with the same speed. The ratio of maximum heights reached by the two bodies if they roll without shipping is

A

` 1 `

B

` ( 2 ) /(sqrt 5 ) `

C

` ( 14 ) /( 15 ) `

D

` ( 4 ) /(5 ) `

Text Solution

Verified by Experts

` KE _ (sph ) = (1)/(2) mv ^ 2 + (1)/(2) I omega ^ 2 = (1)/(2) mv ^ 2 + (1)/(2) ((2)/(5) mR ^ 2 ) ((v^ 2 )/(R^ 2)) `
` = (1)/(2) mv ^ 2 ( 1 + (2 ) /(5)) = (7)/(5) ((1)/(2) mv^ 2) `
maximum ht ` = h_ (sph ) `
` mgh _ (sph ) = ( 7 ) /(5) (( 1 )/(2) mv ^ 2) rArr h _ (sph ) = ( 7 ) /(5) ((v^ 2 )/(2g)) `
Similarly
` h_(cyl) = (3 )/(2) ((v^ 2 )/(2g)) rArr (h_(sph))/(h_(cyl)) = (7//5)/(3//2)= ( 14 ) /(15 ) `
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