Rotational Motion

JEE Main level, single correct, medium

268 of 280

Question 268 of 280

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 sinθcsinθs\dfrac{sin{\theta }_{\text{c}}}{sin{\theta }_{\text{s}}} is :

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Answer: (D) 1514\dfrac{15}{14}

a=g sinθ(1+I/mR2)\text{a}=\dfrac{\text{g sin}\theta }{\left(1+\text{I/}{\text{mR}}^{2}\right)}

aS=g sinθs(1+2/5){\text{a}}_{\text{S}}=\dfrac{\text{g sin}{\theta }_{\text{s}}}{\left(1+2/5\right)}

aC=gsinθC(1+1/2){\text{a}}_{\text{C}}=\dfrac{g sin{\theta }_{\text{C}}}{\left(1+1/2\right)}

Now, aS = aC

gsinθS(75)=gsinθC(32)\dfrac{g sin{\theta }_{\text{S}}}{\left(\dfrac{7}{5}\right)}=\dfrac{g sin{\theta }_{\text{C}}}{\left(\dfrac{3}{2}\right)}

57sinθS=23sinθC\dfrac{5}{7}\text{sin}{\theta }_{\text{S}}=\dfrac{2}{3}\text{sin}{\theta }_{\text{C}}

∴sinθCsinθS=5×37×2=1514∴\dfrac{sin{\theta }_{\text{C}}}{sin{\theta }_{\text{S}}}=\dfrac{5\times 3}{7\times 2}=\dfrac{15}{14}

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