3.  Two blocks A and B each of mass 1 2 k g is connected by a massless inextensible string and kept on horizontal surface.  Coefficient of friction between block and surface is shown in figure.  A force F = kt (Where k = 1 N/s and t is time in secon D)  applied on A.  Then (g = 10 m/s2 )

A)  work done by friction force on block B is zero in time interval t = 0 to t = 3s.
B)  work done by friction force on block A is zero in time interval t = 0 to t = 3s.
C)  work done by tension on B is also zero in time interval t = 0 to t = 3s.
D)  speed of blocks at t = 10s is 27.5 m/s.

Dear student
Maximum friction that can act on A is f1=μsN=0.4×12×10=2NMaximum friction that can act on B is f2=μsN=0.2×12×10=1Nso as both the blocks will move together so they will start moving when appkied force is equal to 3Nthat is  t=3 sectill three seconds no work is done by the friction on both the blocks as their displacement is zero.Also work  done by the tension in the thread is zero for the same reason.After 3 seconds both the blocks move with common acceleration Kinetic friction on block A: f1=μkN=0.2×12×10=1NKinetic friction on block B: f2=μkN=0.2×12×10=1NNet force on A and B together is F=t-(1+1)=t-2Impulse of this force from t=3 to t=10 second is J=310(t-2)dt=t22-2t103=(50-20)-(92-6)=30+6-4.5=36-4.5=31.5 Ns31.5=change im momentum31.5=1v-0v=31.5m/sRegards

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