# Referring to figure (a) and (b) : (1) reading of spring balance in (a) is 8 g and in (b) is also 8 g (2) reading of spring balance in (a) is 8 g and in (b), it is less than 8 g (3) reading in (a) is less than 8 g and in (b), it is 8 g (4) reading in both (a) and (b) is less than 8 g

Consider that the two masses are hanging from the two ends of a cord running over a smooth fixed pulley.
Considering the masses are unequal:
${m}_{1}g-T={m}_{1}a\phantom{\rule{0ex}{0ex}}T-{m}_{2}g={m}_{2}a\phantom{\rule{0ex}{0ex}}Adding\phantom{\rule{0ex}{0ex}}a=\frac{\left({m}_{1}-{m}_{2}\right)}{{m}_{1}+{m}_{2}}g\phantom{\rule{0ex}{0ex}}T=\frac{2{m}_{1}{m}_{2}g}{{m}_{1}+{m}_{2}}$
Then the tension on the string connecting the pulley and balance is twice the tension on the string connecting the two bodies.
Thus the tension in the string connecting the pulley and balance is
${T}_{1}=\frac{4{m}_{1}{m}_{2}g}{{m}_{1}+{m}_{2}}$

Hence the reading on the balances would be
Case (a)
$\frac{4\left(6\right)\left(2\right)}{8}g=6g$
Case (b)
$\frac{4\left(4\right)\left(4\right)}{8}g=8g$
Thus option (3) is correct.

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