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LOM-06- Subjective UnSolved Level-II

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Ans a): 1/2*(5gd) b)P2/27m2g3 A block B of mast M is held at rest on a rough horizontal table. The coefficient of friction between B and the table is 1/2. One end of a light inextensible string is attached to B. The string passes over a small smooth pulley fixed at the edge of the table and is attached to a panicle Q at mass m which hangs freely in equilibrium, as shown in the diagram. It is given that m = 1/2 M. The system it released from rest. Find the speed of the block when it has moved a distance d on the table. It is given instead that m = 1/2 M. The system it released from rest and immediately a force, acting directly towards the policy, is applied to the block. This force acts with constant power P When B has moved a distance x. its speed is v. The string becomes slack before B reaches the pulley. Show that until the string becomes slack, dv/dx = P/mv2\" at the instant when the string becomes slack, v = P/3mg\" Find the distance that B has moved at the instant when the string becomes slack. Solution a)9.81(3M) - T = (3M)a 29.43M - T = 3Ma T=29.43M - 3Ma----eq1 T - FR = Ma FR=RN =(1/2)(9.81M) N T - (4.905M) = Ma T=Ma + 4.905M----eq2 Solve both eqs simultaneously for acceleration a m/s2 29.43M - 3Ma=Ma + 4.905M 29.43M - 4.905M=4Ma 24.525M = 4Ma a=6.13 m/s2 2ad = v2 - u2 2ad = v2 - 0 v2=2(6.13)d v2=12.26d v=3.5d m/s v=1/25gd m/s .

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- Ans a): 1/2*(5gd) b)P2/27m2g3 A block B of mast M is held at rest on a rough horizontal table. The coefficient of friction between B and the table is 1/2. One end of a light inextensible string is attached to B. The string passes over a small smooth pulley fixed at the edge of the table and is attached to a panicle Q at mass m which hangs freely in equilibrium, as shown in the diagram. It is given that m = 1/2 M. The system it released from rest. Find the speed of the block when it has moved a distance d on the table. It is given instead that m = 1/2 M. The system it released from rest and immediately a force, acting directly towards the policy, is applied to the block. This force acts with constant power P When B has moved a distance x. its speed is v. The string becomes slack before B reaches the pulley. Show that until the string becomes slack, dv/dx = P/mv2" at the instant when the string becomes slack, v = P/3mg" Find the distance that B has moved at the instant when the string becomes slack. Solution a)9.81(3M) - T = (3M)a 29.43M - T = 3Ma T=29.43M - 3Ma----eq1 T - FR = Ma FR=RN =(1/2)(9.81M) N T - (4.905M) = Ma T=Ma + 4.905M----eq2 Solve both eqs simultaneously for acceleration a m/s2 29.43M - 3Ma=Ma + 4.905M 29.43M - 4.905M=4Ma 24.525M = 4Ma a=6.13 m/s2 2ad = v2 - u2 2ad = v2 - 0 v2=2(6.13)d v2=12.26d v=3.5d m/s v=1/25gd m/s

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