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NEET
Exam
NEET
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Physics
Chapter
Center of Mass, Momentum and Collision

NEET · Physics · Center of Mass, Momentum and Collision

A block of mass 2 kg moving with a speed of 4 m s ^ -1 on a...

A block of mass 22 kg moving with a speed of 44 m s−1^{-1} on a frictionless horizontal surface collides elastically with an identical block initially at rest. The second block is attached to one end of a relaxed ideal spring of spring constant 3232 N m−1^{-1}, with its other end fixed to a rigid wall. The maximum compression of the spring is:

Options

  1. A12\dfrac{1}{\sqrt{2}} m
  2. B11 m
  3. C2\sqrt{2} m
  4. D0.250.25 m

Correct answer

B. 11 m

Step-by-step solution

Since the collision is perfectly elastic and the blocks have identical masses, they exchange their velocities upon collision.

Velocity of the second block just after the collision, v=4v = 4 m s−1^{-1}.

By conservation of mechanical energy for the second block and spring system:

12mv2=12kx2\dfrac{1}{2} m v^2 = \dfrac{1}{2} k x^2

Substituting the given values (m=2m = 2 kg, v=4v = 4 m s−1^{-1}, k=32k = 32 N m−1^{-1}):

12×2×(4)2=12×32×x2\dfrac{1}{2} \times 2 \times (4)^2 = \dfrac{1}{2} \times 32 \times x^2

16=16x216 = 16 x^2

x2=1⇒x=1x^2 = 1 \Rightarrow x = 1 m.

Answer: 11 m
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