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Two blocks $A(5kg)$ and $B(2kg)$ attached to the ends of a spring constant $1120N/m$ are placed on a smooth horizontal plane with the spring undeformed. Simultaneously velocities of $3m/s$ and $10m/s$ along the line of the spring in the same direction are imparted to $A$ and $B$ then
when the extension of the spring is maximum the velocities of $A$ and $B$ are zero.
the maximum extension of the spring is $25cm.$
maximum extension and maximum compression occur alternately.
Both $(B)$ and $(C)$
Solution
At max. extension both should move with equal velocity.
By momentum conservation,
$\therefore(5 \times 3)+(2 \times 10)=(5+2) \mathrm{V} \mathrm{V}=5 \mathrm{m} / \mathrm{sec}$
Now, by energy conservation
$\frac{1}{2} 5 \times 3^{2}+\frac{1}{2} \times 2 \times 10^{2}$
$=\frac{1}{2}(5+2) \mathrm{V}^{2}+\frac{1}{2} \mathrm{k} \mathrm{x}^{2}$
Put $V$ and $k$
$\therefore X_{\max }=1 / 4 m=25 \mathrm{cm}$
