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 Two block of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is  
 [IIT(Scr.)-2002]
  • a)
    30 m/s
  • b)
    20 m/s
  • c)
    10 m/s
  • d)
    5 m/s
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two block of masses 10 kg and 4 kg are connected by a spring of neglig...
Velocity of heavier block after the impulse = 14m/s
Velocity of lighter block after the impulse = 0 m/s
Thus velocity of COM = 14 x 10 + 0 x 4  / 10 + 4 = 10m/s
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Understanding the Problem
In this scenario, we have two blocks with masses of 10 kg and 4 kg connected by a spring on a frictionless surface. An impulse is applied to the 10 kg block, giving it a velocity of 14 m/s towards the lighter block.
Calculating Total Mass
- Mass of Block 1 (m1) = 10 kg
- Mass of Block 2 (m2) = 4 kg
- Total mass (M) = m1 + m2 = 10 kg + 4 kg = 14 kg
Impulse and Velocity of the Heavier Block
- The impulse gives the heavier block (10 kg) a velocity of 14 m/s.
- This velocity is directed toward the 4 kg block.
Calculating Center of Mass Velocity
To find the velocity of the center of mass (V_cm), we can use the formula:
V_cm = (m1 * v1 + m2 * v2) / (m1 + m2)
Where:
- v1 = velocity of the heavier block = 14 m/s
- v2 = velocity of the lighter block = 0 m/s (initially at rest)
Substituting the values:
V_cm = [(10 kg * 14 m/s) + (4 kg * 0 m/s)] / (14 kg)
V_cm = (140 kg*m/s) / (14 kg)
Final Result
- V_cm = 10 m/s
Thus, the velocity of the center of mass is 10 m/s, making the correct answer option (c).
This explains why option 'C' is the correct answer to the problem.
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Two block of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of the centre of mass is [IIT(Scr.)-2002]a)30 m/sb)20 m/sc)10 m/sd)5 m/sCorrect answer is option 'C'. Can you explain this answer?
Question Description
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