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Question

# A block of mass M is pulled along a horizontal surface by applying a force at an angle with the horizontal. The friction coefficient between the block and the surface is μ. If the block travels at a uniform velocity, then the work done by this applied force during a displacement d of the block is—

A
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B
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C
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D
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Solution

## The correct option is C Forces on the block are (i) Its weight Mg, (ii) The normal force N (iii) The applied force F and (iv) The kinetic friction μN. The forces are shown in figure. As the block moves with a uniform velocity, the forces add up to zero. Taking horizontal and vertical components, Fcosθ=μNand Fsinθ+N=Mg Eliminating N from these equations, Fcosθ=μ(Mg−Fsinθ) or, F=μMgcosθ+μsinθ. The work done by this force during a displacement d is W=Fdcosθ=μMgdcosθcosθ+μsinθ

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