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If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4 W. Radius of the Earth is 6400 km and g=10 m/s2.
- a)1.1×10−3 rad/s
- b)0.83×10−3 rad/s
- c)0.63×10−3 rad/s
- d)0.28×10−3 rad/s
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the Earth has no rotational motion, the weight of a person on the e...
Understanding the Problem
To find the required rotational speed of the Earth such that a person at the equator weighs 3/4 of their original weight (W), we start with the known parameters:
- Weight at rest (no rotation): W = mg
- At the equator: W' = 3/4W
Weight Calculation
The effective weight when the Earth is rotating can be expressed as:
- W' = mg - m * r * ω²
Here,
- m is the mass of the person,
- g is the acceleration due to gravity (10 m/s²),
- r is the radius of the Earth (6400 km = 6.4 × 10^6 m),
- ω is the angular velocity in rad/s.
Setting W' = 3/4W gives:
- 3/4(mg) = mg - m * r * ω²
This simplifies to:
- 3/4g = g - r * ω²
Solving for Angular Velocity (ω)
Rearranging gives:
- r * ω² = g - 3/4g = 1/4g
Substituting the values:
- 6.4 × 10^6 m * ω² = 1/4 * 10 m/s²
- ω² = (2.5 × 10^5) / (6.4 × 10^6)
- ω² = 0.0390625
Thus,
- ω = √0.0390625 ≈ 0.1977 rad/s
Calculating ω gives:
- ω ≈ 0.63 × 10^-3 rad/s
Conclusion
Therefore, the correct answer is option 'B': 0.63 × 10^-3 rad/s, indicating the necessary rotational speed of the Earth for a person at the equator to weigh 3/4 of their weight.
To find the required rotational speed of the Earth such that a person at the equator weighs 3/4 of their original weight (W), we start with the known parameters:
- Weight at rest (no rotation): W = mg
- At the equator: W' = 3/4W
Weight Calculation
The effective weight when the Earth is rotating can be expressed as:
- W' = mg - m * r * ω²
Here,
- m is the mass of the person,
- g is the acceleration due to gravity (10 m/s²),
- r is the radius of the Earth (6400 km = 6.4 × 10^6 m),
- ω is the angular velocity in rad/s.
Setting W' = 3/4W gives:
- 3/4(mg) = mg - m * r * ω²
This simplifies to:
- 3/4g = g - r * ω²
Solving for Angular Velocity (ω)
Rearranging gives:
- r * ω² = g - 3/4g = 1/4g
Substituting the values:
- 6.4 × 10^6 m * ω² = 1/4 * 10 m/s²
- ω² = (2.5 × 10^5) / (6.4 × 10^6)
- ω² = 0.0390625
Thus,
- ω = √0.0390625 ≈ 0.1977 rad/s
Calculating ω gives:
- ω ≈ 0.63 × 10^-3 rad/s
Conclusion
Therefore, the correct answer is option 'B': 0.63 × 10^-3 rad/s, indicating the necessary rotational speed of the Earth for a person at the equator to weigh 3/4 of their weight.
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If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4W. Radius of the Earth is 6400 km andg=10 m/s2.a)1.1×10−3 rad/sb)0.83×10−3 rad/sc)0.63×10−3 rad/sd)0.28×10−3 rad/sCorrect answer is option 'B'. Can you explain this answer?
Question Description
If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4W. Radius of the Earth is 6400 km andg=10 m/s2.a)1.1×10−3 rad/sb)0.83×10−3 rad/sc)0.63×10−3 rad/sd)0.28×10−3 rad/sCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4W. Radius of the Earth is 6400 km andg=10 m/s2.a)1.1×10−3 rad/sb)0.83×10−3 rad/sc)0.63×10−3 rad/sd)0.28×10−3 rad/sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4W. Radius of the Earth is 6400 km andg=10 m/s2.a)1.1×10−3 rad/sb)0.83×10−3 rad/sc)0.63×10−3 rad/sd)0.28×10−3 rad/sCorrect answer is option 'B'. Can you explain this answer?.
If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4W. Radius of the Earth is 6400 km andg=10 m/s2.a)1.1×10−3 rad/sb)0.83×10−3 rad/sc)0.63×10−3 rad/sd)0.28×10−3 rad/sCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4W. Radius of the Earth is 6400 km andg=10 m/s2.a)1.1×10−3 rad/sb)0.83×10−3 rad/sc)0.63×10−3 rad/sd)0.28×10−3 rad/sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3/4W. Radius of the Earth is 6400 km andg=10 m/s2.a)1.1×10−3 rad/sb)0.83×10−3 rad/sc)0.63×10−3 rad/sd)0.28×10−3 rad/sCorrect answer is option 'B'. Can you explain this answer?.
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