Question

The time period of a vibrating spring due to a mass $m$ is $T$. For twice of its mass, the new time period will be:

• A. $\sqrt{2}T$
• B. $2\sqrt{2}T$
• C. $4T$
• D. $5T$

Answer 1

Answer: (A)

The time period of spring
$T=2\pi \sqrt{\left(\frac{m}{R}\right)}...(1)$
$k=$ force constant of spring
again $T^{\prime }=2\pi \sqrt{\left(\frac{m^{\prime }}{k}\right)}$
$=2\pi \sqrt{\left(\frac{2m}{k}\right)}$
$\left(\because m^{\prime }=2m\right)\dots (2)$
From equations (1) and (2)
$\therefore T^{\prime }=\sqrt{2}T$