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What is the magnitude of gravitational force between the earth and a 1kg object in its surface. ( mass of earth is 6.4×10^6m, G=6.67×19^-11Nm^2/kg^2)?
Most Upvoted Answer
What is the magnitude of gravitational force between the earth and a 1...
Given,
m1 = 1kg
m2 = 6× 10^24 kg
radius of the earth = 6.4 ×10^6 m
now,
f = G m1 m2 / (r)^2
f = 6.67× 10^-11 × 1 × 6× 10^24 /(6.4 ×10^6 )^2
f = 6.67× 10^-11 × 1 × 6× 10^24/ 6.4× 6.4 × 10^12
f = 6.67 ×1 × 6 ×10^13/6.4× 6.4 × 10^12
f = 6.67 × 1×6×10/6.4×6.4
f = 400.2/40.96
f = 9.7705078125
f = 9.8 N..
m1 = 1kg
m2 = 6× 10^24 kg
radius of the earth = 6.4 ×10^6 m
now,
f = G m1 m2 / (r)^2
f = 6.67× 10^-11 × 1 × 6× 10^24 /(6.4 ×10^6 )^2
f = 6.67× 10^-11 × 1 × 6× 10^24/ 6.4× 6.4 × 10^12
f = 6.67 ×1 × 6 ×10^13/6.4× 6.4 × 10^12
f = 6.67 × 1×6×10/6.4×6.4
f = 400.2/40.96
f = 9.7705078125
f = 9.8 N..
Community Answer
What is the magnitude of gravitational force between the earth and a 1...
Calculation of Gravitational Force between the Earth and a 1kg Object
Given Data:
- Mass of the Earth (m1) = 6.4 × 10^6 kg
- Mass of the object (m2) = 1 kg
- Gravitational constant (G) = 6.67 × 10^-11 Nm^2/kg^2
Formula:
The formula to calculate the magnitude of gravitational force is given by Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant,
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
Calculation:
In this case, the object is on the surface of the Earth. The distance between the centers of the Earth and the object is equal to the radius of the Earth, which is given as 6.4 × 10^6 m.
Substituting the given values into the formula, we have:
F = (6.67 × 10^-11 Nm^2/kg^2) * (6.4 × 10^6 kg) * (1 kg) / (6.4 × 10^6 m)^2
Simplifying the equation:
F = (6.67 × 10^-11 Nm^2/kg^2) * (6.4 × 10^6 kg) * (1 kg) / (6.4 × 10^6 m) * (6.4 × 10^6 m)
F = (6.67 × 10^-11 N) * (1)
F = 6.67 × 10^-11 N
Result:
The magnitude of gravitational force between the Earth and a 1kg object on its surface is approximately 6.67 × 10^-11 Newtons.
Given Data:
- Mass of the Earth (m1) = 6.4 × 10^6 kg
- Mass of the object (m2) = 1 kg
- Gravitational constant (G) = 6.67 × 10^-11 Nm^2/kg^2
Formula:
The formula to calculate the magnitude of gravitational force is given by Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant,
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
Calculation:
In this case, the object is on the surface of the Earth. The distance between the centers of the Earth and the object is equal to the radius of the Earth, which is given as 6.4 × 10^6 m.
Substituting the given values into the formula, we have:
F = (6.67 × 10^-11 Nm^2/kg^2) * (6.4 × 10^6 kg) * (1 kg) / (6.4 × 10^6 m)^2
Simplifying the equation:
F = (6.67 × 10^-11 Nm^2/kg^2) * (6.4 × 10^6 kg) * (1 kg) / (6.4 × 10^6 m) * (6.4 × 10^6 m)
F = (6.67 × 10^-11 N) * (1)
F = 6.67 × 10^-11 N
Result:
The magnitude of gravitational force between the Earth and a 1kg object on its surface is approximately 6.67 × 10^-11 Newtons.
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