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Question

A block placed on a horizontal surface is being pushed by a force F making an angle θ with the vertical as shown in figure. The coefficient of friction between block and surface is μ. The force required to slide the block with uniform velocity on the floor is

A
μmg(sinθμcosθ)
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B
(sinθμcosθ)μmg
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C
μmg
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D
None of these
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Solution

The correct option is A μmg(sinθμcosθ)
For vertical equibrium of the block,
N=Fcosθ+mg(1)
While for horizontal motion in equilibrium
FsinθμN=0or Fsinθμ=N(2)
From Eqs. (1) and (2),
Fsinθ=μ(Fcosθ+mg)
i.e., F=μmg(sinθμcosθ)
Hence, the correct answer is option (a).

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