Q. A body of mass m is kept on a rough horizontal surface (coefficient of friction = m) A horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by F, where F is :

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A

$∣ ∣ F ∣ ∣ = m g + μ m g$

21%

B

$∣ ∣ F ∣ ∣ = μ m g$

13%

C

$∣ ∣ F ∣ ∣ \leq m g 1 + μ^{2}$

60%

D

$∣ ∣ F ∣ ∣ = m g$

6%

Solution:

$N = m g, F = f$
Resultant $= N^{2} + f^{2}$
$= (m g)^{2} + f^{2} \leq m g 1 + μ^{2}$