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Question

In the system shown in figure blocks A and B have mass m1=2kg and m2=267 kg respectively. Pulley having moment of inertia I = 0.11 kg m2 can rotate without friction about a fixed axis. Inner and outer radii of pulley are a = 10 cm and b = 15 cm respectively. B is hanging with the thread wrapped around the pulley, while A lies on a rough inclined plane.


Coefficient of friction being μ=310

ColumnIColumnIIP.Tension in the thread connecting block Aw.26NQ.Tension in the thread connecting block Bx.2ms2R accelerationofAR.Acceleration of Ay.3ms2S.Acceleration of Bz.17N


A

P-w, Q-z, R-x, S-y

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B

P-z, Q-w, R-y, S-x

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C

P-z, Q-w, R-x, S-y

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D

P-z, Q-z, R-y, S-y

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Solution

The correct option is C

P-z, Q-w, R-x, S-y


When the system is released, weight m2g tries to rotate the pulley in clockwise direction while down the plane component m1g sin 30 of weight of block A tries to rotate it anticlockwise. But moment produced by m2g is greater, therefore, the pulley has tendency to rotate clockwise. Let its angular acceleration be 'α'. Then acceleration of blocks A and B will be equal to a α (up the plane) and b α (ertically downwards) respectively. Let tension in threads connected with blocks A and B be T1 and T2 respectively.

Considering free body diagrams

For forces on block A, N=m1gcos30 , ...(i)
T1m1g sin30μN=m1(aα)...(ii)
For forces on block B,m2gT2=m2(b α)...(iii)

Taking moments of forces acting on pulley, about axis of rotation, T2bT1a=1α ...(iv)

From above equation N=103N

T1=17N,T2=26Nα=20radsec2

Acceleration of block, A=aα=2ms2 (up the plane)

Acceleration of block, B=b α=3ms2 (downward)


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