Question

The time period of a light loaded spring is $3.5$ seconds. On changing the load by $1$ kg, the period decreases by $0.5$ seconds. The initial load on the spring is

• A. $3\frac{10}{13}$ kg
• B. $4\frac{10}{13}$ kg
• C. $5\frac{10}{13}$ kg
• D. $6\frac{10}{13}$ kg

Answer 1

The correct option is A $3\frac{10}{13}$ kg

$T=2\pi \sqrt{\frac{m}{k}}$
$3.5=2\pi \sqrt{\frac{m}{k}}$..........[1]
$3=2\pi \sqrt{\frac{m-1}{k}}$.................[2]

From [1] and [2];
$\frac{m}{m-1}=(\frac{7}{6}{)}^2$
$36m=49m-49$
$49=13m$
$m=\frac{49}{13}=3\frac{10}{13}$