question_answer

A block of 2 kg is suspended from the ceiling through a massless spring of spring constant k = 100 N/m. What is the elongation of the spring? If another 1 kg is added to the block, what would be the further elongation?

Answer:

(i) \[m=2kg,\,\,K=100N/m,\,\,x=?\] we know, \[F=-kx\Rightarrow mg=-kx\] \[\Rightarrow x=\frac{mg}{k}=\frac{2\times 10}{100}=\frac{20}{100}=0.2m\] (ii) Let further elongation be 'x' then \[F=-k(x+x')\Rightarrow mg=-k(x+x')\] \[\Rightarrow 3\times 10=100(0.2+x')\] \[\Rightarrow 30=100(0.5+x')\] \[\frac{3}{10}-0.2=x'\Rightarrow x'=\frac{1}{10}=0.1m\]