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  4. 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 θc/ sin θs) is :

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Q. A cylinder of mass $M_c$ and sphere of mass $M_s$ 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 $\frac{\sin \,\theta_{c}}{\sin\,\theta_{s}} $ is :Physics Question Image

JEE MainJEE Main 2014System of Particles and Rotational Motion

Solution:

$\frac{g\,\sin\,\theta_{c}}{1+\frac{1}{2}}=\frac{g\,\sin\,\theta_{s}}{1+\frac{2}{5}}$
$\frac{\sin\theta_{c}}{\sin\,\theta_{s}}=\frac{3/ 2}{7/ 5}=\frac{15}{14}$