Question

Two blocks of mass 2 kg and 4 kg respectively are placed on smooth horizontal surface. They are connected by a spring of force constant ‘k’. Initially the spring was unstretched and velocities of 1 m/s and 2 m/s are imparted in opposite direction as shown. Velocity (in m/s) of centre of mass when extension in spring is maximum is n. Value of n, is​

Answer 1

Answer:

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Explanation:

At the maximum extension, the velocity of both the blocks will be same.

Let the common velocity of the blocks is v.

From conservation of linear momentum, it can be written as,

(3+6)×v=6×2−3×1

v=1m/s

Let the maximum extension in the spring is x.

From conservation of mechanical energy, it can be written as,

2

1

×3×(1)

2

+

2

1

×6×(2)

2

=

2

1

×200×(x)

2

+

2

1

×9×(1)

2

x

2

=

100

18

=0.3m

=30cm

Thus, the maximum extension in the spring is 30cm.