Question

Two blocks of masses 3 kg and 6 kg are connected by an ideal spring and are placed on a frictionless horizontal surface. The 3 kg block is imparted a speed of $2m{s}^{-1}$ towards left (consider left as positive direction)

When the velocity of 3 kg block is $\frac{2}{3}m{s}^{-1}$	Velocity of centre of mass is $\frac{2}{3}m{s}^{-1}$
When the velocity of 6 kg block is $\frac{2}{3}m{s}^{-1}$	Deformation of the spring is zero
When the speed of 3 kg block is minimum	Deformation of the spring is maximum
When the speed of 6 kg block is maximum	Both the blocks are at rest with respect to each other

• A. D$\to$ 2,1, C$\to$ 1, B$\to$ 4, 3,1, A$\to$ 4, 3,1
• B. A$\to$ 2,1, B$\to$ 1, C$\to$ 4, 3,1, D$\to$ 4, 3,1
• C. B$\to$ 2,1, D$\to$ 1, A$\to$ 4, 3,1, C$\to$ 4, 3,1
• D. C$\to$ 2,1, A$\to$ 1, D$\to$ 4, 3,1, B$\to$ 4, 3,1

Answer 1

Answer: (A)

D$\to$ 2,1, C$\to$ 1, B$\to$ 4, 3,1, A$\to$ 4, 3,1

$m_1=3kg$;
$m_2=6kg$;
$v_1=2m/s$;
$v_2=0m/s$;
$(m_1+m_2)v_{cm}=m_1{v}_1+m_2{v}_2$ ....(1)

Putting the values in eqn(1), we get $v_{cm}=\frac{2\times 3}{3+6}=\frac{6}{9}=\frac{2}{3}m/s$;

When maximum deformation of the spring occurs, both the blocks will have equal velocities which are again equal to $v_{cm}$;
(B) and (A) will map to 4,3,1.

The $6kg$ block will have its maximum velocity at the extreme position in its left i.e. when the elongation in the spring is minimum.
And as no external force is acting on the system, the velocity of the center of mass would remain same as $2/3$ m/s.