Question

A block of mass $m$ is lying on an inclined plane. The coefficient of friction between the plane and the block is $\mu$. The force $\left(F_1\right)$ required to move the block up the inclined plane will be :

• A. $mg\sin \theta +\mu mg\cos \theta$
• B. $mg\cos \theta -\mu mg\sin \theta$
• C. $mg\sin \theta -\mu mg\cos \theta$
• D. $mg\cos \theta +\mu mg\sin \theta$

Answer 1

The correct option is A $mg\sin \theta +\mu mg\cos \theta$

Body tends to move upward i.e., in the direction of $f_1$ hence frictional for $f_r$ is in the opposible direction of $f_2$

FBD of block

as for equillibrium

$N_2$ $mg\cos \theta =f_r=$ $\mu mg\cos \theta$

minimum force $f_1$ such that block start moving up ward

$F_1=mg\sin \theta +f_r$

$F_1=mg\sin \theta +\mu mgcos\theta$.