Question

A 2 kg block is dropped from a height $0.4m$ on a spring of force constant $k=1960N/m$.The maximum compression of spring is

• A. $0.1m$
• B. $0.2m$
• C. $0.3m$
• D. $0.4m$

Answer 1

The correct option is A $0.1m$

By law of conservation of energy , we have loss in gravitational potential energy=gain in elastic potential energy
$\Rightarrow mg(h+x)=\frac{1}{2}k{x}^2$
$2\times 10(0.4+x)=\frac{1}{2}\times 1960\times x^2$
$\Rightarrow 8+20x=980x^2$
$\Rightarrow 980x^2-20x-8=0$
Solving ,we get
$x=0.1m$