Question

A spring balance has a scale reading from 0 to 50 kg. The length of the scale is 20 cm. A body suspended to the spring balance when displaced and released oscillates with a period of $0.6$ second. The mass off the body is:

• A. 15 kg
• B. 22 kg
• C. 50 kg
• D. 0.5 kg

Answer 1

The correct option is B 22 kg

According to the question,

The maximum mass scale can read $M=50kg$

The maximum displcement of spring $=$

length of scale, $l=20cm=0.2m$

$T$ (time period) $=0.6s$

Maximum force exerted on the spring $F=mg$

So,

$g=$acceleration due to gravity $=9.8m/s^2$

$F=50\times 9.8=490$

Since, speing constant,

$k=\frac{F}{l}$

$=\frac{490}{0.2}$

$=2450N{m}^{-1}$

$m$ is suspended from the balance

$T=2\pi \sqrt{\frac{m}{k}}$

Since,

$m={\left(\frac{T}{2\pi }\right)}^2\times k$

$={\left(\frac{0.6}{2\times 3.14}\right)}^2\times 2450$

$\approx 22kg$