Question

A massless spring of force constant 1000 N/m is compressed a distance of 20cm between discs of 8kg and 2kg, spring is not attached to discs. The system is given an initial velocity 3m/s perpendicular to length of spring as shown in figure. What is ground frame speed of 2 kg block (in m/s) when spring regains its natural length.

• A. 4 m/s
• B. 5 m/s
• C. 1 m/s
• D. None of these

Answer 1

The correct option is B

5 m/s

Let $v_1$ and $v_2$ are the velocities along the spring of A and B when spring regains it natural lenght the 2$v_1$ = 8$v_2$ (Conservation of momentum) ------------------(i)

$\frac{1}{2}2v_1^2+\frac{1}{2}8v_2^2=\frac{1}{2}1000(\frac{20}{100}{)}^2$ --------------------(ii)

From (i) and (ii) $v_1$ = 4m/s, $v_2$ = 1 m/s

Ground frame speed of A

= $\sqrt{v^2+v_1^2}=\sqrt{3^2+4^2}=5m/s$