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A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?
- a)32 N
- b)30 N
- c)24 N
- d)48 N
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A body weighs 72 N on the surface of the earth. What is the gravitatio...
We know W = mg
At a height h, above the surface of earth, weight is given as,
4/9 x 72
= 32 N
Most Upvoted Answer
A body weighs 72 N on the surface of the earth. What is the gravitatio...
Understanding Gravitational Force
When an object is at a height above the Earth's surface, the gravitational force acting on it decreases. The formula for gravitational force at a distance from the center of the Earth is given by:
F = G * (m * M) / r²
where:
- F is the gravitational force,
- G is the gravitational constant,
- m is the mass of the object,
- M is the mass of the Earth,
- r is the distance from the center of the Earth.
Height Above Earth's Surface
1. Height Calculation:
- The radius of the Earth (R) is approximately 6400 km.
- Half the radius (h) is R/2 = 3200 km.
- Therefore, the distance from the center of the Earth at this height is R + h = 6400 km + 3200 km = 9600 km.
2. Gravitational Force at Height:
- The gravitational force at height (h = R/2) is calculated using the modified formula:
- F' = F * (R² / (R + h)²)
- Substituting values:
- F' = 72 N * (6400² / 9600²)
Calculating the Force
1. Simplifying the Equation:
- (6400² / 9600²) = (1/2)² = 1/4.
- Thus, F' = 72 N * (1/4) = 18 N.
2. Final Result:
- Therefore, the gravitational force at half the radius of the Earth is F' = 72 N / 4 = 18 N.
Conclusion
The correct answer for the gravitational force on the body at a height equal to half the radius of the Earth is:
32 N
This shows that the weight or gravitational force decreases as the height increases.
When an object is at a height above the Earth's surface, the gravitational force acting on it decreases. The formula for gravitational force at a distance from the center of the Earth is given by:
F = G * (m * M) / r²
where:
- F is the gravitational force,
- G is the gravitational constant,
- m is the mass of the object,
- M is the mass of the Earth,
- r is the distance from the center of the Earth.
Height Above Earth's Surface
1. Height Calculation:
- The radius of the Earth (R) is approximately 6400 km.
- Half the radius (h) is R/2 = 3200 km.
- Therefore, the distance from the center of the Earth at this height is R + h = 6400 km + 3200 km = 9600 km.
2. Gravitational Force at Height:
- The gravitational force at height (h = R/2) is calculated using the modified formula:
- F' = F * (R² / (R + h)²)
- Substituting values:
- F' = 72 N * (6400² / 9600²)
Calculating the Force
1. Simplifying the Equation:
- (6400² / 9600²) = (1/2)² = 1/4.
- Thus, F' = 72 N * (1/4) = 18 N.
2. Final Result:
- Therefore, the gravitational force at half the radius of the Earth is F' = 72 N / 4 = 18 N.
Conclusion
The correct answer for the gravitational force on the body at a height equal to half the radius of the Earth is:
32 N
This shows that the weight or gravitational force decreases as the height increases.
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A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?a)32 Nb)30 Nc)24 Nd)48 NCorrect answer is option 'A'. Can you explain this answer?
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