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Calculate angular velocity of the earth so that acceleration due to gravity at 60o latitude becomes zero. (radius of the earth = 6400 km , gravitational acceleration at poles = 10 m s−2 , cos60o = 0.5)
  • a)
    7.8 × 10−2 rad s−1
  • b)
    0.5 × 10−3 rad s−1
  • c)
    1 × 10−3 rad s−1
  • d)
    2.5 × 10−3 rad s−1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Calculate angular velocity of the earth so that acceleration due to gr...
According to Question
Acceleration due to gravity at 60o latitude = g60 = 0 ms−2
Acceleration due to gravity at pole = g = 10 m s−2
Now Relation between acceleration due to gravity (g) and latitude (λ)
g' = g − Reωcos2λ
Here g'= Acceleration due to gravity at λ latitude
g = Acceleration due to gravity at pole
Re = 6400 km = Radius of earth
Re = 6400 km = 6.4 × 106 m
λ = Latitude of position
ω = Angular velocity of earth
Apply the above g and λ relation
g60 = g − Reωcos2 60o
Put the all known values in the above relation
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Calculate angular velocity of the earth so that acceleration due to gr...
First, we need to find the distance of a point on the surface of the Earth at 60° latitude from the axis of rotation. This can be done using trigonometry:

cos(60°) = x / 6400 km
x = 6400 km * cos(60°) = 3200 km

Next, we can calculate the acceleration due to gravity at 60° latitude using the formula:

g = G * M / r^2

where g is the acceleration due to gravity, G is the gravitational constant (6.67 x 10^-11 N * m^2 / kg^2), M is the mass of the Earth (5.97 x 10^24 kg), and r is the distance from the center of the Earth to the point in question.

At the poles, the acceleration due to gravity is 10 m/s^2, so we can use this information to set up the following equation:

10 = G * 5.97 x 10^24 / (6400 km)^2

Now, we can calculate the angular velocity of the Earth at 60° latitude when the acceleration due to gravity becomes zero. The acceleration due to gravity is zero when the centripetal acceleration is equal to the gravitational acceleration at that latitude:

a = v^2 / r

where a is the centripetal acceleration, v is the tangential velocity, and r is the distance from the axis of rotation.

Since the acceleration due to gravity is zero, the centripetal acceleration becomes:

v^2 / r = 0

Therefore, the angular velocity of the Earth at 60° latitude when the acceleration due to gravity becomes zero is 0.
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Calculate angular velocity of the earth so that acceleration due to gravity at 60olatitude becomes zero. (radius of the earth = 6400 km, gravitational acceleration at poles = 10 m s−2, cos60o = 0.5)a)7.8 × 10−2 rad s−1b)0.5 × 10−3 rad s−1c)1 × 10−3 rad s−1d)2.5 × 10−3 rad s−1Correct answer is option 'D'. Can you explain this answer?
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Calculate angular velocity of the earth so that acceleration due to gravity at 60olatitude becomes zero. (radius of the earth = 6400 km, gravitational acceleration at poles = 10 m s−2, cos60o = 0.5)a)7.8 × 10−2 rad s−1b)0.5 × 10−3 rad s−1c)1 × 10−3 rad s−1d)2.5 × 10−3 rad s−1Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Calculate angular velocity of the earth so that acceleration due to gravity at 60olatitude becomes zero. (radius of the earth = 6400 km, gravitational acceleration at poles = 10 m s−2, cos60o = 0.5)a)7.8 × 10−2 rad s−1b)0.5 × 10−3 rad s−1c)1 × 10−3 rad s−1d)2.5 × 10−3 rad s−1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate angular velocity of the earth so that acceleration due to gravity at 60olatitude becomes zero. (radius of the earth = 6400 km, gravitational acceleration at poles = 10 m s−2, cos60o = 0.5)a)7.8 × 10−2 rad s−1b)0.5 × 10−3 rad s−1c)1 × 10−3 rad s−1d)2.5 × 10−3 rad s−1Correct answer is option 'D'. Can you explain this answer?.
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