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Two blocks of masses 6 kg and 4 kg are placed on a frictionless surface and connected by a spring. If the heavier mass is given a velocity of 14 m/s in the direction of lighter one, then the velocity gained by the centre of mass will be
- a)7.4 m/s
- b)14 m/s
- c)8.4 m/s
- d)10 m/s
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two blocks of masses 6 kg and 4 kg are placed on a frictionless surfac...
Since the spring is massless, no force will be exerted on the smaller mass.
Its velocity will be zero.
The velocity gained by the centre of mass -
Its velocity will be zero.
The velocity gained by the centre of mass -
Most Upvoted Answer
Two blocks of masses 6 kg and 4 kg are placed on a frictionless surfac...
Given:
- Mass of the first block (heavier mass) = 6 kg
- Mass of the second block (lighter mass) = 4 kg
- Velocity of the first block = 14 m/s
To find:
The velocity gained by the center of mass.
Solution:
The center of mass velocity can be found using the concept of conservation of momentum.
Step 1: Find the initial momentum
The initial momentum of the system can be calculated as the sum of the momentum of each block.
Initial momentum = (mass of the first block × velocity of the first block) + (mass of the second block × velocity of the second block)
Since the second block is initially at rest, the initial momentum is given by:
Initial momentum = (mass of the first block × velocity of the first block)
Initial momentum = (6 kg × 14 m/s) = 84 kg⋅m/s
Step 2: Find the final momentum
The final momentum of the system can be calculated using the concept of conservation of momentum.
Final momentum = (mass of the first block × velocity of the first block) + (mass of the second block × velocity of the second block)
Since the blocks are connected by a spring and no external forces are acting on the system, the final momentum of the system is equal to the initial momentum.
Final momentum = Initial momentum = 84 kg⋅m/s
Step 3: Find the velocity of the center of mass
The velocity of the center of mass can be calculated by dividing the final momentum of the system by the total mass of the system.
Center of mass velocity = Final momentum / (mass of the first block + mass of the second block)
Center of mass velocity = 84 kg⋅m/s / (6 kg + 4 kg)
Center of mass velocity = 84 kg⋅m/s / 10 kg
Center of mass velocity = 8.4 m/s
Therefore, the velocity gained by the center of mass is 8.4 m/s, which is option (c).
- Mass of the first block (heavier mass) = 6 kg
- Mass of the second block (lighter mass) = 4 kg
- Velocity of the first block = 14 m/s
To find:
The velocity gained by the center of mass.
Solution:
The center of mass velocity can be found using the concept of conservation of momentum.
Step 1: Find the initial momentum
The initial momentum of the system can be calculated as the sum of the momentum of each block.
Initial momentum = (mass of the first block × velocity of the first block) + (mass of the second block × velocity of the second block)
Since the second block is initially at rest, the initial momentum is given by:
Initial momentum = (mass of the first block × velocity of the first block)
Initial momentum = (6 kg × 14 m/s) = 84 kg⋅m/s
Step 2: Find the final momentum
The final momentum of the system can be calculated using the concept of conservation of momentum.
Final momentum = (mass of the first block × velocity of the first block) + (mass of the second block × velocity of the second block)
Since the blocks are connected by a spring and no external forces are acting on the system, the final momentum of the system is equal to the initial momentum.
Final momentum = Initial momentum = 84 kg⋅m/s
Step 3: Find the velocity of the center of mass
The velocity of the center of mass can be calculated by dividing the final momentum of the system by the total mass of the system.
Center of mass velocity = Final momentum / (mass of the first block + mass of the second block)
Center of mass velocity = 84 kg⋅m/s / (6 kg + 4 kg)
Center of mass velocity = 84 kg⋅m/s / 10 kg
Center of mass velocity = 8.4 m/s
Therefore, the velocity gained by the center of mass is 8.4 m/s, which is option (c).
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Two blocks of masses 6 kg and 4 kg are placed on a frictionless surface and connected by a spring. If the heavier mass is given a velocity of 14 m/s in the direction of lighter one, then the velocity gained by the centre of mass will bea)7.4 m/sb)14 m/sc)8.4 m/sd)10 m/sCorrect answer is option 'C'. Can you explain this answer?
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