Two blocks A(5 kg) and B(2 kg) attached to | vedclass

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(D) At maximum extension,both blocks move with the same velocity $V$ relative to the ground.By the law of conservation of linear momentum:$m_A u_A + m

Vedclass · Accepted Answer

Both $(B)$ and $(C)$.

Vedclass · Answer

(D) At maximum extension,both blocks move with the same velocity $V$ relative to the ground.By the law of conservation of linear momentum:$m_A u_A + m_B u_B = (m_A + m_B) V$$(5 	imes 3) + (2 	imes 10) = (5 + 2) V$$15 + 20 = 7V \implies 35 = 7V \implies V = 5 \ m/s$.Now,by the law of conservation of mechanical energy:Initial Energy = Final Energy (at max extension)$\frac{1}{2} m_A u_A^2 + \frac{1}{2} m_B u_B^2 = \frac{1}{2} (m_A + m_B) V^2 + \frac{1}{2} k x_{max}^2$$\frac{1}{2} (5)(3^2) + \frac{1}{2} (2)(10^2) = \frac{1}{2} (5 + 2)(5^2) + \frac{1}{2} (1120) x_{max}^2$$22.5 + 100 = 87.5 + 560 x_{max}^2$$122.5 - 87.5 = 560 x_{max}^2$$35 = 560 x_{max}^2$$x_{max}^2 = \frac{35}{560} = \frac{1}{16}$$x_{max} = \frac{1}{4} \ m = 0.25 \ m = 25 \ cm$.Since the system is conservative and oscillates,maximum extension and maximum compression occur alternately. Thus,both $(B)$ and $(C)$ are correct.

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