Rotational Motion

JEE Main level, single correct, medium

181 of 280

Question 181 of 280

A uniform disc of radius RR and mass MM is free to rotate only about its axis. A string is wrapped over its rim and a body of mass mm is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is:

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Answer: (D) 2mg2m+M\dfrac{2mg}{2m+M}

mg−T=mamg-T=ma

RT=IαRT=I\alpha

RT=MR22.aRRT=\dfrac{M{R}^{2}}{2}.\dfrac{a}{R}

T=Ma2T=\dfrac{Ma}{2}

mg−Ma2=mamg-\dfrac{Ma}{2}=ma

mg=a(M2+m)mg=a\left(\dfrac{M}{2}+m\right)

mg=a(M+2m2)mg=a\left(\dfrac{M+2m}{2}\right)

a=2mgM+2ma=\dfrac{2mg}{M+2m}

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