Question

The scale of a spring balance reading from $0$ to $10kg$ is $0.25m$ long. A body suspended from the balance oscillates vertically with a period of $\pi /10s$. The mass suspended is neglected then the mass of the spring is:

• A. $10kg$
• B. $0.98kg$
• C. $5kg$
• D. $20kg$

Answer 1

The correct option is B $0.98kg$

Time period T =$2\pi \sqrt{\frac{m}{k}}=0.1\times \pi$
Angular velocity $\omega =\frac{2\pi }{T}=20rad/s$
for 'k' the spring constant at maximum reading x=0.25 m extension:
$M=10kg$
$Mg=-kx$
$k$- spring constant ; $g$ -acceleration due to gravity
$k=392.4N/m$
Now
$2\pi \sqrt{\frac{m}{k}}=0.1\times \pi$
putting the value of $k$ .
$m=0.98kg$