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A mass m slips along the wall of a semispherical surface of radius R. The velocity at the bottom of the surface is [ MP PMT 1993]

(1) Rg

(2) 2Rg

(3) 2πRg

(4) πRg

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Three different objects of masses m1, m2 and m3 are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of 

(1) m1:m2:m3

(2) m1:2m2:3m3

(3) 1 : 1 : 1

(4) 1m1:1m2:1m3 

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Which of the following graph depicts spring constant k versus length l of the spring correctly

(1)
(2)
(3)
(4)
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