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Question:

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 sinθc/sinθs is :

√87

√1514

1514

87

Solution:

a=gsinθ1+k^2/r^2
Substituting k for cylinder as √(1/2)r and for sphere as √(2/5)r we get
The acceleration of a cylinder rolling down an incline is ac=2/3gsinθc
Similarly, for sphere, as=5/7gsinθs
Since, the two accelerations are equal,
sinθc/sinθs=15/14