Question

Find the reading of the spring balance for the figure shown. Take $g=10m/s^2$

• A. $1.2kg$
• B. $2.4kg$
• C. $3.6kg$
• D. $4.8kg$

Answer 1

The correct option is D $4.8kg$

The given spring balance arrangement can be converted to string arrangement as shown

As we know that the spring balance reads the spring force $kx$ which is equivalent to tension $T$ in the string.

So, from the FBDs of both the blocks we have
$6g-T=6a$........(i)
and,
$T-4g=4a$.......(ii)
On solving (i) & (ii), we get
$2g=10a\Rightarrow a=\frac{2g}{10}=2m/s^2$
$\therefore$ from FBD of $6Kg$ we have
$T=6(g-a)=6\times 8=48N$
So, the reading in spring balance is
Equivalent mass = $\frac{48}{g}=4.8kg$


Alternate:

$\text{a}=\frac{\text{supporting force- opposing force}}{\text{Total mass}}$
$=\frac{6g-4g}{10}=\frac{2g}{10}=2m/s^2$
For $6kg$ mass ; $T=6(g-a)=6\times 8=48N$
$\therefore$ Equivalent mass = $\frac{48}{g}=4.8kg$