Question

In the figure, all pulleys are massless and strings are light.
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(a) 1 kg block}& \text{(p)}\text{will remain stationary}\\ \text{(b) 2 kg block}& \text{(q)}\text{will move down}\\ \text{(c) 3 kg block}& \text{(r)}\text{will move up}\\ \text{(a) 4 kg block}& \text{(s)}5{\text{m/s}}^2\\ & \text{(t)}10{\text{m/s}}^2\end{array}$

• A. $a-t,b-p,c-s,d-q$
• B. $a-p,b-t,c-s,d-q$
• C. $a-r,t,b-p,c-q,d-q,s$
• D. $a-r,b-p,c-q,d-p$

Answer 1

The correct option is C $a-r,t,b-p,c-q,d-q,s$

$a\to r,b\to p,c\to q,d\to p,s$


As pulleys are massless,
$80=F=2T_1\Rightarrow T_1=40\text{N}$
$T=T_2=\frac{T_1}{2}=40\text{N}$
For FBD of $1\text{kg}$
$20-g=a\Rightarrow a=10{\text{m/s}}^2\uparrow$
For FBD of $2\text{kg}$
$20-2g=a\Rightarrow a=0{\text{m/s}}^2$
For FBD of $3\text{kg}$
$3g-20=3a\Rightarrow a=\frac{10}{3}{\text{m/s}}^2\downarrow$
For FBD of $4\text{kg}$
$4g-20=4a\Rightarrow a=5{\text{m/s}}^2\downarrow$