Question

The coefficient of friction between the block and the horizontal surface is $\mu$. The block moves towards right under of horizontal force $F$. Sometime later another force $P$ is applied to the block making an angle $\theta$ (such that $\tan \theta =\mu )$ with vertical as shown in figure. After application of force $P$, the acceleration of block shall.

• A. Increase
• B. Decrease
• C. Remains same
• D. Information insufficient for drawing inference

Answer 1

The correct option is C Remains same

$f_1-$ frictional force

$f_1=\mu mg$

$a_1=\frac{F-\mu mg}{m}$

when $P$ is applied frictional force is $f_2$

$f_2=\mu (mg+P\cos \theta )$

let in this situation acceleration is $a_2$, then we have;

$F+P\sin \theta -f_2=m{a}_2$

$a_2=\frac{F+P\sin \theta -f_2}{m}$$=\frac{F+P\sin \theta -\mu (mg+P\cos \theta )}{m}$

$a_2=\frac{F-\mu mg}{m}+\frac{P(\sin \theta -\mu \cos \theta )}{m}$

$a_2=a_1+\frac{P(\sin \theta -\mu \cos \theta )}{m}$ ..............(2)

Given that $\tan \theta =\mu$

$\sin \theta =\mu \cos \theta$

So, from eq. (2);

$a_2=a_1$ (remains same)