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Question

Let F, FN and f denote the magnitude of the contact force, normal force and the friction force exerted by one surface on the other kept in contact. If none of these is zero
a.
F>FN
b. F>f
c. FN>f
d. FN−f<F<FN+f

A
a and c are correct
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B
b and c are correct
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C
a, b and d are correct
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D
only a and b are correct
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Solution

The correct option is D a, b and d are correct
By definition, contact force is the square root of the sum of squares of normal force and friction. Contact force is net force between the body and surface. Normal force and friction force are normal to each other (so pythagoras theorem). So it is greater than normal force and friction individually.
Also on constructing a right triangle using friction and normal force as its perpendicular sides one can easily show that option D is correct using basic triangle inequalities.

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