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The block of mass m initially at x = 0 is acted upon by a horizontal force F = a - bx2 (where a>μmg), as shown in the figure. The co-efficient of friction between the surfaces of contact is μ. The net work done on the block is zero, if the block travels a distance of

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a

x=3(a−μmg)b

b

x=3(a+μmg)b

c

x=2(a−μmg)b

d

x=2(a+μmg)b

answer is A.

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Detailed Solution

The friction force and external force will do work on the block Wtotal =Wf+WF=−μmgx+∫0x a−bx2dxAs total work is equal to zero; 0=(−μmg+a)x−bx33⇒x=3(a−μmg)b

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The block of mass m initially at x = 0 is acted upon by a horizontal force F = a - bx2 (where a>μmg), as shown in the figure. The co-efficient of friction between the surfaces of contact is μ. The net work done on the block is zero, if the block travels a distance of