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A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.?
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A stone weight 100N on the surface of earth. The ratio of its weight a...
Solution:
We know that the weight of an object is given by the formula:
Weight = mass x acceleration due to gravity
Where acceleration due to gravity (g) is given by:
g = G x M / r^2
where G is the universal gravitational constant, M is the mass of the earth, and r is the distance from the center of the earth.
Weight at the surface of the earth:
Weight of the stone at the surface of the earth is given as 100N.
Weight at half the radius of the earth:
At a height of half the radius of the earth, the distance from the center of the earth is r/2. Therefore, acceleration due to gravity at this height is given by:
g' = G x M / (r/2)^2 = 4 x G x M / r^2
Weight of the stone at this height is given by:
Weight' = mass x g'
Since mass is constant, we can write:
Weight' / Weight = g' / g
Substituting the values of g and g', we get:
Weight' / Weight = 4
Therefore, weight of the stone at half the radius of the earth is 4 times its weight at the surface of the earth.
Weight at a depth of half the radius of the earth:
At a depth of half the radius of the earth, the distance from the center of the earth is 3r/2. Therefore, acceleration due to gravity at this depth is given by:
g'' = G x M / (3r/2)^2 = 4/9 x G x M / r^2
Weight of the stone at this depth is given by:
Weight'' = mass x g''
Since mass is constant, we can write:
Weight'' / Weight = g'' / g
Substituting the values of g and g'', we get:
Weight'' / Weight = 4/9
Therefore, weight of the stone at a depth of half the radius of the earth is 4/9 times its weight at the surface of the earth.
Ratio of weight at half the radius to depth of half the radius:
Weight' / Weight'' = (g' / g) / (g'' / g) = (g' / g) x (g / g'') = 4 x (9/4) = 9
Therefore, the ratio of weight of the stone at half the radius of the earth to its weight at a depth of half the radius of the earth is approximately 9.
Hence, the answer is option D) 0.9.
We know that the weight of an object is given by the formula:
Weight = mass x acceleration due to gravity
Where acceleration due to gravity (g) is given by:
g = G x M / r^2
where G is the universal gravitational constant, M is the mass of the earth, and r is the distance from the center of the earth.
Weight at the surface of the earth:
Weight of the stone at the surface of the earth is given as 100N.
Weight at half the radius of the earth:
At a height of half the radius of the earth, the distance from the center of the earth is r/2. Therefore, acceleration due to gravity at this height is given by:
g' = G x M / (r/2)^2 = 4 x G x M / r^2
Weight of the stone at this height is given by:
Weight' = mass x g'
Since mass is constant, we can write:
Weight' / Weight = g' / g
Substituting the values of g and g', we get:
Weight' / Weight = 4
Therefore, weight of the stone at half the radius of the earth is 4 times its weight at the surface of the earth.
Weight at a depth of half the radius of the earth:
At a depth of half the radius of the earth, the distance from the center of the earth is 3r/2. Therefore, acceleration due to gravity at this depth is given by:
g'' = G x M / (3r/2)^2 = 4/9 x G x M / r^2
Weight of the stone at this depth is given by:
Weight'' = mass x g''
Since mass is constant, we can write:
Weight'' / Weight = g'' / g
Substituting the values of g and g'', we get:
Weight'' / Weight = 4/9
Therefore, weight of the stone at a depth of half the radius of the earth is 4/9 times its weight at the surface of the earth.
Ratio of weight at half the radius to depth of half the radius:
Weight' / Weight'' = (g' / g) / (g'' / g) = (g' / g) x (g / g'') = 4 x (9/4) = 9
Therefore, the ratio of weight of the stone at half the radius of the earth to its weight at a depth of half the radius of the earth is approximately 9.
Hence, the answer is option D) 0.9.
Community Answer
A stone weight 100N on the surface of earth. The ratio of its weight a...
3.6
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A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.?
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A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.?.
A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.?.
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A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.?, a detailed solution for A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.? has been provided alongside types of A stone weight 100N on the surface of earth. The ratio of its weight at the height of half the radius of earth to it's weight at a depth of half the radius of earth will be approximately. A) 3.6 B) 2.2 C) 1.8 D) 0.9. Plz ans fast.? theory, EduRev gives you an
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