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Question

# A block of mass m is placed on a rough horizontal surface. The coefficient of friction between them is μ. An external horizontal force is applied to the block and its magnitude is gradually increased. The force exerted by the block on the surface is R then :

A
the magnitude of R will gradually increase.
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B
Rmgμ2+1
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C
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D
the angle made by R with the vertical tan1μ.
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Solution

## The correct options are A the magnitude of R will gradually increase. B R≤mg√μ2+1 D the angle made by R with the vertical ≤tan−1μ.N=Mg;fs=Nμfs=mgμ→ maximum value of friction possible Now R= resultant of N&fsNow, value of fs keeps on increasing and it is equal to the external force f untilf=fsafter that friction force is constantly mgμSo R increases graduallyR=√(mgμ)2+(mg)2R=mg√μ2+1→ maximum value of RNow tanθ=fsN⇒tanθ=mgclmg⇒tanθ=μθ (maximum value of θ) =tan−1(μ)

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