Question

A frictionless pulley of negligible weight is suspended from a spring balance as shown in fig. Masses of $1kg$ and $5kg$ are tied to the ends of string which passes over the pulley. The masses move due to gravity. The reading of the balance will be:

• A. more than $6kg$
• B. $6kg$
• C. less than $3kg$
• D. less than $6kg$ and more than $3kg$

Answer 1

The correct option is D less than $6kg$ and more than $3kg$

Let a tension $T$ be generated in the string with the masses.Let the masses have the acceleration $a$.

equation of motion-

$T-1g=1a$

$5g-T=5a$

$\Rightarrow$ $a=\frac{4g}{6}$

Now let a tension $T_1$ be generated in the string connecting the spring.As the pulley is massless we have $T_1=2T$

Hence the reading shown by the spring balance is $2TN$ or $\frac{20}{6}kg$.

So,option $D$ is correct