A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v . The sphere and the cylinder reaches upto maximum heights h₁ and h₂ , respectively, above the initial level. The ratio h₁: h₂ is

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A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v . The sphere and the cylinder reaches upto maximum heights h₁ and h₂ , respectively, above the initial level. The ratio h₁: h₂ is n 10 . The value of n is______.

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Gain in P.E. = Loss in K.E. mgh = 1 2 mv ^2 (1+ K ^2 R ^2 ) h 1+ K ^2 R ^2 h ₁ ~h ₂ = 1+ 2 5 1+1 = 7 5 2 = 7 10 n =7

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v . The sphere and the cylinder reaches upto maximum heights h₁ and h₂ , respectively, above the initial level. The ratio h₁: h₂ is n 10 . The value of n is______.

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