Question

Initially both blocks are at rest on a horizontal surface and string is just tight. At $t=0$, two constant horizontal forces $F_1$ and $F_2$ start acting on blocks as shown. $f_1$ and $f_2$ are friction forces acting on 10 kg and 20 kg block (coefficient of friction between blocks and ground are 0.5). Values of $F_1$ and $F_2$ are given in column - I. Then match magnitudes of $f_1$, $f_2$ and direction of $\overrightarrow{f_1}$ with corresponding values of $F_1$ and $F_2$ given in column - II $[g=10m/s^2]$.



$\begin{array}{cccc}& Column-I& & Column-II\\ \left(A\right)& F_2=120N,F_1=40N& \left(p\right)& f_2=100N,f_1=20N\\ \left(B\right)& F_2=160N,F_1=40N& \left(q\right)& f_2=20N,f_1=50N\\ \left(C\right)& F_2=60N,F_1=90N& \left(r\right)& f_2=70N,f_1=50N\\ \left(D\right)& F_2=20N,F_1=90N& \left(s\right)& unitvectorindirectionof\overrightarrow{f_1}is\hat{i}\\ & & \left(t\right)& unitvectorindirectionof\overrightarrow{f_1}is-\hat{i}\end{array}$

• A. A-p,s; B-p,t; C-q,s; D-q,s
• B. A-p,s; B-p,s; C-q,t; D-q,s
• C. A-p,s; B-p,t; C-q,s; D-r,s
• D. A-p,s; B-p,t; C-q,t; D-q,t

Answer 1

The correct option is A A-p,s; B-p,t; C-q,s; D-q,s

As in all the conditions:
$|\overrightarrow{F_1}+\overrightarrow{F_2}|<|f_1{|}_{max}+|f_2{|}_{max}$
So, both blocks wont move in any case.
$|f_1{|}_{max}=50N$ and $|f_2{|}_{max}=100N$
To understand each situation, make first F.B.D of that block on which External force is exceeding friction force as additional force will be provided by tension and then FBD of other block.
Option A:

Option B:

Option C:

Option D:
So,

A	B	C	D
p,s	p,t	q,s	q,s