Question

A spring of natural length $l$ and spring constant $50N/m$ is kept on a horizontal frictionless table with one end attached to a rigid support. First the spring was compressed by $10cm$ and then released to hit a ball of mass $20g$ kept at a distance l from the rigid support. if after hitting the ball, the natural length of the spring is restored, what is the speed with which the ball moved? (Ignore the air resistance)

• A. 5 m/s
• B. 7 m/s
• C. 25 m/s
• D. 50 m/s
• E. 2500 m/s

Answer 1

Answer: (A)

A spring of spring constant $50N/m$ is attached to a rigid wall. A $20g$ ball is placed on the horizontal table as shown in figure

If spring is compressed then potential energy
$U=\frac{1}{2}k{x}^2$
When spring hit the ball, it transfer all its potential energy to kinetic energy of ball
$\frac{1}{2}k{x}^2=K{E}_{ball}$
$\Rightarrow \frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2$
$\Rightarrow v=\sqrt{\frac{k{x}^2}{m}}$
Given, $x=20cm,m=20g$ and $v=50N/m$
$\Rightarrow v=\sqrt{\frac{50\times {\left(20\times 10^{-2}\right)}^2}{20\times 10^{-3}}}$
$=\sqrt{25}=5m/s$