Question

Let F , Fn and f denote the magnitude of contact force, normal force and the friction 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.

Answer 1

Answer ⇒ Option (a). (b). and (d).

Explanation ⇒  We know that the contact force is the vector sum of the Normal reaction and the Friction force. Also both the Frictional force and the normal reaction is perpendicular to each other.

Thus, Contact force will always be greater than the Normal Reaction as well as the Frictional force like Hypotenuse is always greater than the perpendicular and base of the Right angled Triangles.

Therefore, Option (a). and (b). is correct.

Now, We know that sometimes coefficient of friction is greater than 1 and sometimes it is less than 1. If it is greater than 1 then frictional force will be greater than Normal reaction but when it is less than 1 than the friction will be less than 1. So nothing can be said about that options until the full conditions are not given. Thus, we cannot say that this option(c).  is correct.

Now, we know that F (Contact Force) is greater than both the Fn and f.

∴ F  > Fn - f .   -----eq(i)

Also, we know that maximum value of the resulting vector is the sum of the individual vectors magnitude.

∴ F  ≤ Fn + f   ----(ii).

Therefore, Option (d). is also correct

Hope it helps.