Question

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.

• A. When the extension of the spring is maximum the velocities of A and B are zero.
• B. The maxium extension of the spring is 25cm.
• C. The first maximum compression occurs $3\pi /56$ seconds after start.
• D. Maximum extension and maximum compression occur alternately.

Answer 1

Answer: (B), (D)

The correct options are
B The maxium extension of the spring is 25cm.
D Maximum extension and maximum compression occur alternately.

At Maximum extension , both blocks should move with same velocity, By Principle of conservation of Momentum,$m_1\times v_1+m_2\times v_2=M\times V$

$(5\times 3)+(10\times 2)=(5+2)\times V$
$\therefore V=5\frac{m}{s}$
Now by Principle of conservation of energy,
$\frac{1}{2}{m}_1\times {v_1}^2+\frac{1}{2}{m}_2\times {v_2}^2=\frac{1}{2}M\times V^2+\frac{1}{2}k\times x^2$
$\therefore \frac{1}{2}(5\times 3^2)+\frac{1}{2}(2\times {10}^2)=\frac{1}{2}(5+2)\times 5^2+\frac{1}{2}(1120\times x^2)$
$\therefore x=25cm$