Question

A system consists of two identical cubes, each of mass 3 kg, linked together by a compressed weightless spring of force constant $1000N{m}^{-1}$. The cubes are also connected by a thread which is burnt at a certain moment. At what minimum value of initial compression $x_0$ (in cm) of the spring will the lower cube bounce up after the thread is burnt through?

• A. 10
• B. 9
• C. 8
• D. 7

Answer 1

The correct option is B 9

$\begin{array}{c}foreqpositoionof3kg=kx\\ \Rightarrow 20=1000x\\ \Rightarrow x=\frac{30}{1000}=2cm\\ \Rightarrow \left(\frac{x_0-3}{100}\right)k=3g\\ \Rightarrow \left(\frac{x_0-3}{100}\right)1000=30\\ \Rightarrow x_0=6cm\\ \therefore initialcompression=x_0+3\\ =9cm\\ Hence,\\ optionBiscorrectanswer.\end{array}$