Question

A $2$ kg block is dropped from a height of $0.4$ m on a spring of force constant $K=1960N{m}^{-1}$. The maximum compression of the spring is?

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

Answer 1

The correct option is A $0.1$m

Given:

Mass of the body is $\left(m\right)=2Kg$

spring's constant $\left(K\right)=1960$ N/m

Let comparetion of spring is $x$

$mg(h+x)=\frac{1}{2}Kx²$

$2mgh+2mgx=Kx²$

$Kx²-2mgx-2mgh=0$

$\Rightarrow 1960x²-2\times 2\times 9.8\times x-2\times 2\times 9.8\times 0.4=0$

$\Rightarrow 1960x²-39.2x-15.68=0$

After solving this quadratic equations , we get $x=0.1$ m