Question

In the arrangement shown below, the reading of the spring balance will be

• A. 2 kg
• B. 5 kg
• C. $\frac{15}{4}$ kg
• D. Zero

Answer 1

The correct option is C $\frac{15}{4}$ kg


Let T be the tension in the string.
$m_1=3kg$
$m_2=5kg$
For the block of mass $m_1$:
$T–m_{1}g=m_{1}a$
$\Rightarrow T–3g=3a$ …..(i)
For the block of mass $m_2$:
$m_{2}g–T=m_{2}a$
$\Rightarrow 5g–T=5a$ …..(ii)
Adding (i) and (ii):
$\Rightarrow 2g=8a$
$\Rightarrow a=\frac{g}{4}m/s^2$
Substituting value of a in (ii):
$5g–T=5\frac{g}{4}$
$\Rightarrow \Rightarrow T=5g-\frac{5g}{4}$
$\Rightarrow \Rightarrow T=\frac{15g}{4}$
$\therefore$ Corresponding reading in spring balance $=\frac{T}{g}=\frac{\left(\frac{15}{4}\right)g}{g}=\frac{15}{4}kg$
Hence, the correct answer is option (3).