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What is the length of a metre stick moving parallel to its length when its mass is 3/2 times of its rest mass.
- a)0.67 m
- b)0.4 m
- c)0.9 m
- d)0.1 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the length of a metre stick moving parallel to its length when...
The mass of the rod is 3/2 times its rest mass, that is
The length of meter stick moving parallel to its length, according to length contraction formula.
L0 = 1m
L = 1 × 0.667 = 0.67m
The correct answer is: 0.67 m
The length of meter stick moving parallel to its length, according to length contraction formula.
L0 = 1m
L = 1 × 0.667 = 0.67m
The correct answer is: 0.67 m
Most Upvoted Answer
What is the length of a metre stick moving parallel to its length when...
Given:
- The mass of the meter stick at rest is "m".
- The mass of the meter stick in motion is (3/2)m.
- The length of the meter stick is not mentioned.
To solve this problem, we need to apply the concept of length contraction in special relativity.
1. Length Contraction:
According to the theory of special relativity, an object moving relative to an observer will appear shorter in the direction of motion. This phenomenon is known as length contraction.
The formula for length contraction is given by:
L' = L * √(1 - v^2/c^2)
where L' is the length of the object as measured by the observer in motion, L is the rest length of the object, v is the velocity of the object, and c is the speed of light.
2. Applying the Formula:
In this case, the meter stick is moving parallel to its length. Let's assume the rest length of the meter stick is "L".
Given that the mass of the meter stick in motion is (3/2)m, it implies that the meter stick is moving with a velocity close to the speed of light.
Using the length contraction formula, we can calculate the length of the meter stick in motion.
L' = L * √(1 - v^2/c^2)
Since the velocity of the meter stick is close to the speed of light, we can approximate v^2/c^2 to be 1.
L' = L * √(1 - 1)
L' = L * √(0)
L' = 0
This implies that the length of the meter stick in motion is effectively zero. Therefore, option 'A' (0.67m) cannot be the correct answer.
3. Conclusion:
The correct answer is not provided in the given options. The length of the meter stick moving parallel to its length when its mass is (3/2)m will be effectively zero due to length contraction in special relativity.
- The mass of the meter stick at rest is "m".
- The mass of the meter stick in motion is (3/2)m.
- The length of the meter stick is not mentioned.
To solve this problem, we need to apply the concept of length contraction in special relativity.
1. Length Contraction:
According to the theory of special relativity, an object moving relative to an observer will appear shorter in the direction of motion. This phenomenon is known as length contraction.
The formula for length contraction is given by:
L' = L * √(1 - v^2/c^2)
where L' is the length of the object as measured by the observer in motion, L is the rest length of the object, v is the velocity of the object, and c is the speed of light.
2. Applying the Formula:
In this case, the meter stick is moving parallel to its length. Let's assume the rest length of the meter stick is "L".
Given that the mass of the meter stick in motion is (3/2)m, it implies that the meter stick is moving with a velocity close to the speed of light.
Using the length contraction formula, we can calculate the length of the meter stick in motion.
L' = L * √(1 - v^2/c^2)
Since the velocity of the meter stick is close to the speed of light, we can approximate v^2/c^2 to be 1.
L' = L * √(1 - 1)
L' = L * √(0)
L' = 0
This implies that the length of the meter stick in motion is effectively zero. Therefore, option 'A' (0.67m) cannot be the correct answer.
3. Conclusion:
The correct answer is not provided in the given options. The length of the meter stick moving parallel to its length when its mass is (3/2)m will be effectively zero due to length contraction in special relativity.
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