Questions

# Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed $\upsilon$. What is the net force on the block of mass 2m? (g is the acceleration due to gravity)

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a
3 mg
b
6 mg
c
Zero
d
2 mg

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detailed solution

Correct option is C

Let T1 be tension in string connecting m and 2m and T2 be tension in string connecting 2m and 3m.            Let a be common acceleration of the system.∴  a=F−m+2m+3mgm+2m+3m=F−6m6mAs the system moves with constant speed, therefore, a = 0∴   F−6mg=0  or  F=6mgThe free body diagram of block m is as shown in the figure.The equation of motion of block of mass m isF−T1−mg=0 6mg−T1−mg=0 T1=5mg        −−−(i)The free body diagram of block of mass 2m is as shown in the figure.The equation of motion of block of mass 2m isT1−T2−2mg=0 5mg−T2−2mg=0     Using  i T2=3mgThe free body diagram of block of mass3m is as shown in the figure.The equation of motion of block of mass 3m isT2−3mg=0 T2=3mgNet force on the block of mass 2m isFnet=T1−T2−2mg =5mg−3mg−2mg=0Alternate solutionAs all blocks are moving with constant speed, therefore, acceleration is zero. So net force on each block is zero.

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