Question

A mass of 2 kg falls from a height of 40 cm on a spring of force constant 1960 N/m. The spring is compressed by:

• A. 10 cm
• B. 0.4 cm
• C. 0.01 cm
• D. 0.04 cm

Answer 1

The correct option is A 10 cm

Given,

$Mass=2kg,height=40cm$ Force constant $k=1960N/m$

Let the h be the height from which the mass m falls on the spring of the force constant k and x is the compression on the string.

So, the gain in the elastic potential energy of string is equal to the loss in gravitational potential energy of falling mass,

$\frac{1}{2}k{x}^2=mg(h+x)\Rightarrow \frac{1}{2}1960\times x^2=2\times 9.8(0.40+x)\Rightarrow 980x^2=7.84+19.6x\Rightarrow 980x^2-19.6x-7.84=0$

$x=10cm$