Question

A block of mass $ 2 \,kg $ is dropped from a height of $ 40 \,cm $ on a spring whose force-constant is $ 1960\, N\,m^{-1} $ . The maximum distance through which the spring is compressed by

• A. $ 5 \,cm $
• B. $ 15 \,cm $
• C. $ 20 \,cm $
• D. $ 10 \,cm $

Answer 1

Answer: (D)

$ mg\left(h + x\right)= \frac{1}{2}kx^{2} $
Here, $ m = 2 \,kg $ , $ h = 40\, cm $
$ k = 1960 \,N \,m^{-1} $ and $ g = 10\, ms^{-2} $ .
$ \therefore 2 \times10\left(0.40+x\right)= \frac{1}{2}\times1960\,x^{2} $
On solving, we get $ x = 10\, cm $ .