A cylinder of mass M c and sphere of mass M s are placed at points A and B of two inclines, respectively.…

A cylinder of mass Mc and sphere of mass Ms are placed at points A and B of two inclines, respectively. (See figure). If they roll on the incline without slipping such that their accelerations are the same, then the ratio sin θ c sin θ s  is :
  1. 8 7
  2. 8 7
  3. 15 14
  4. 1 5 1 4

Solution

a = g sin  θ 1 + I/ mR 2

a S = g sin  θ s 1 + 2 / 5

a C = g sin θ C 1 + 1 / 2

Now, aS = aC

g sin θ S 7 5 = g sin θ C 3 2

5 7  sin  θ S = 2 3  sin  θ C

∴    sin θ C sin θ S = 5 × 3 7 × 2 = 1 5 1 4

Asked in: JEE Main 2014 (09 Apr Online)

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