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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
the angle made by R with the vertical will gradually increase.
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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 Rmgμ2+1
D the angle made by R with the vertical tan1μ.
N=Mg;

fs=Nμ

fs=mgμ maximum value of friction possible

Now R= resultant of N&fs

Now, value of fs keeps on increasing and it is equal to the external force f until

f=fs

after that friction force is constantly mgμ

So R increases gradually

R=(mgμ)2+(mg)2

R=mgμ2+1 maximum value of R

Now tanθ=fsNtanθ=mgclmg

tanθ=μ

θ (maximum value of θ) =tan1(μ)

1423764_138244_ans_6df1f76bb89b4823a8a5b66f91a02bc2.png

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