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 $x = 10\, cm$ .