Question

A ball of mass 2 kg moving with velocity 3 m/s, collides with spring of natural length 2 m and force constant 144 N/m. What will be length of compressed spring?

• A. 2 m
• B. 1.65 m
• C. 1 m
• D. 0.5 m

Answer 1

Answer: (B)

1.65 m

Energy of the spring-ball must me conserved.

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

On substituting values,

$\Rightarrow \frac{1}{2}\times 2{\left(3\right)}^2=\frac{1}{2}\times 144{\left(x\right)}^2$

Solving for $x$ we get, $x=0.35m$

So, length of the compressed spring $=2-0.35=1.65m$