Question

A force F is applied to a block of mass 2 kg at some angle as shown in the figure, then

• A. When the block is moving, the force of friction is 8 N.
• B. When the block is stationary, the force of friction is less than 12 N.
• C. $N\ne 0$ for any value of F.
• D. When the block is moving the force of friction is less than 8 N.

Answer 1

The correct option is D When the block is moving the force of friction is less than 8 N.


$N+Fsin\theta =mg\Rightarrow N=mg-Fsin\theta$ $=20-Fsin\theta$
When block is moving, $f={\mu }_{k}N=0.4(20-Fsin\theta )$ $=8-0.4Fsin\theta$
Option A is not correct.
$F_{\left(max\right)}={\mu }_{k}N$
$=0.6\times (mg-Fsin\theta )$
$=0.6(20-Fsin\theta )$
$=12-0.6Fsin\theta \to$ option B is correct.
$N=mg-Fsin\theta$
$N=0\Rightarrow mg=Fsin\theta \to$ This is possible.
As derived in first step, f < & N (while moving )
Option D is correct.