Question

A body of mass $0.1\text{kg}$ moving with a velocity of $10\text{m/s}$ hits a spring of force constant $1000\text{N/m}$ whose one end is fixed to a wall and comes to rest after compressing the spring. The compression of the spring is

• A. $0.4\text{m}$
• B. $0.1\text{m}$
• C. $0.2\text{m}$
• D. $0.5\text{m}$

Answer 1

The correct option is B $0.1\text{m}$

Given:

$k=1000\text{N/m};m=0.1\text{kg};v=10\text{m/s}$

When the body hits the spring, the whole kinetic energy of the body is converted into the spring potential energy.

$\therefore \frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2$

$\Rightarrow x=\sqrt{\frac{m}{k}}\times v=\sqrt{\frac{0.1}{1000}}\times 10$

$\therefore x=0.1\text{m}$