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We have got two vertical track of equal radius One is smooth and other is...

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We have got two vertical track of equal radius One is smooth and other is rough One small solid sphere is to be projected from the bottom of the circular tracks It is seen that when it is projected on the smooth track the minimum linear speed is u to reach the top of the track and in case rough track it is u angular velocity u r where r is the radius of the sphere Assuming no slipping between the sphere and the rough track the ratio of u to u is 1 05 27 05 17

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