Discussion Forum

A mass of 2kg initially at a height of  1.2 m above an uncompressed spring with spring constant $2 \times 10^{4} $ N/m, is released from rest to fall on the spring. Taking the acceleration due to gravity  as 10 m/s² and neglecting the air resistance, the compression of the spring in mm is 

Answer:

Explanation:

 Key idea    when  a mass m is fall from height h on an uncompressed spring then the maximum compression is given by the relation,

 mgh=$\frac{1}{2}kx^{2}$

(principle of energy conservation)

Given, mass of body , m=2kg, height,h=1.2m , spring constant , k= 2 x 10⁴ N/m and acceleration due to gravity , g-10 m/s²

 Then,   $x=\sqrt{\frac{2mgh}{k}}\Rightarrow x=\sqrt{\frac{2\times2\times1.2\times10}{2\times 10^{4}}}$

 $\Rightarrow$       =$4.89 \times 10^{-2} m$   $\approx$ 50mm

So, the correct option is  (c)