Question

A block of mass $20\text{kg}$ is suspended through two light spring balances as shown in figure. Calculate the reading of spring balance $\left(1\right)$ and $\left(2\right)$ respectively.

• A. $200\text{N},400\text{N}$
• B. $400\text{N},200\text{N}$
• C. $0\text{N},200\text{N}$
• D. $200\text{N},200\text{N}$

Answer 1

The correct option is D $200\text{N},200\text{N}$

FBD of each component of spring+block system:


From FBD of block, applying equilibrium condition in vertical direction,
$T_2-mg=0$
$\therefore T_2=mg=20\times 10=200\text{N}...\left(i\right)$

Since spring balances are assumed massless and system is in equilibrium i.e $a=0$
For spring balance $2$,
$T_2-T_1=m_2\times a=0\times 0=0$
$\therefore T_1=T_2=200\text{N}$
Simillarly, for spring balance $1$,
$T^{\prime }-T_1=m_{1}a=0\times 0=0$
$\therefore T^{\prime }=T_1=200\text{N}$

Therefore, reading of both spring balances will show $200\text{N}$