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The height at which a body has one fourth of its weight when it is on the surface of the earth is :-
- a)At a height r where r is the radius of the earth
- b)At a height 2r where r is the radius of the earth
- c)At a height r/2 where r is the radius of the earth
- d)At a height r/4 where r is the radius of the earth
Correct answer is option 'A'. Can you explain this answer?
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Explanation:
To understand why the correct answer is option 'A', let's analyze the concept of weight and its relationship with height.
Weight and Gravity:
Weight is the force with which an object is pulled towards the center of the Earth by gravity. It is given by the equation:
Weight = mass x acceleration due to gravity
The acceleration due to gravity is denoted by 'g' and is approximately 9.8 m/s^2 on the surface of the Earth.
Weight at Different Heights:
When an object is at a height above the surface of the Earth, the force of gravity acting on it decreases. This is because the distance between the object and the center of the Earth increases.
The force of gravity is inversely proportional to the square of the distance between two objects. Therefore, as the height increases, the force of gravity decreases.
Calculating the Height:
Let's assume the weight of the body on the surface of the Earth is W.
According to the question, at a certain height, the body has one-fourth of its weight. This means the weight at that height is one-fourth of the weight on the surface of the Earth.
Weight at height = 1/4 x Weight on the surface of the Earth
Using the equation for weight, we can write:
mass x acceleration due to gravity at height = 1/4 x mass x acceleration due to gravity on the surface of the Earth
The mass cancels out from both sides of the equation, giving:
acceleration due to gravity at height = 1/4 x acceleration due to gravity on the surface of the Earth
Since the acceleration due to gravity at a height is directly proportional to the distance from the center of the Earth, we can write:
distance from the center of the Earth at height = 1/4 x distance from the center of the Earth on the surface of the Earth
The distance from the center of the Earth is equal to the radius of the Earth plus the height. Let's denote the radius of the Earth as 'r' and the height as 'h'. We can rewrite the equation as:
r + h = 1/4 x r
Simplifying the equation:
h = 1/4 x r - r
h = -3/4 x r
As height cannot be negative, we take the magnitude:
h = 3/4 x r
Therefore, the height at which the body has one-fourth of its weight is 3/4 times the radius of the Earth.
Conclusion:
The correct answer is option 'A' - At a height 'r', where 'r' is the radius of the Earth.
To understand why the correct answer is option 'A', let's analyze the concept of weight and its relationship with height.
Weight and Gravity:
Weight is the force with which an object is pulled towards the center of the Earth by gravity. It is given by the equation:
Weight = mass x acceleration due to gravity
The acceleration due to gravity is denoted by 'g' and is approximately 9.8 m/s^2 on the surface of the Earth.
Weight at Different Heights:
When an object is at a height above the surface of the Earth, the force of gravity acting on it decreases. This is because the distance between the object and the center of the Earth increases.
The force of gravity is inversely proportional to the square of the distance between two objects. Therefore, as the height increases, the force of gravity decreases.
Calculating the Height:
Let's assume the weight of the body on the surface of the Earth is W.
According to the question, at a certain height, the body has one-fourth of its weight. This means the weight at that height is one-fourth of the weight on the surface of the Earth.
Weight at height = 1/4 x Weight on the surface of the Earth
Using the equation for weight, we can write:
mass x acceleration due to gravity at height = 1/4 x mass x acceleration due to gravity on the surface of the Earth
The mass cancels out from both sides of the equation, giving:
acceleration due to gravity at height = 1/4 x acceleration due to gravity on the surface of the Earth
Since the acceleration due to gravity at a height is directly proportional to the distance from the center of the Earth, we can write:
distance from the center of the Earth at height = 1/4 x distance from the center of the Earth on the surface of the Earth
The distance from the center of the Earth is equal to the radius of the Earth plus the height. Let's denote the radius of the Earth as 'r' and the height as 'h'. We can rewrite the equation as:
r + h = 1/4 x r
Simplifying the equation:
h = 1/4 x r - r
h = -3/4 x r
As height cannot be negative, we take the magnitude:
h = 3/4 x r
Therefore, the height at which the body has one-fourth of its weight is 3/4 times the radius of the Earth.
Conclusion:
The correct answer is option 'A' - At a height 'r', where 'r' is the radius of the Earth.
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The height at which a body has one fourth of its weight when it is on the surface of the earth is :-a)At a height r where r is the radius of the earthb)At a height 2r where r is the radius of the earthc)At a heightr/2where r is the radius of the earthd)At a heightr/4where r is the radius of the earthCorrect answer is option 'A'. Can you explain this answer?
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