The weight of a body on the surface of the earth is 392N .What will be the weight of this body on a planet whose mass is double that of the earth and radius is four times that of the earth
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To find the weight of the body on the new planet, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects,
and r is the distance between the centers of the two objects.
Let's denote the mass of the body on the surface of the Earth as m1 and the mass of the body on the new planet as m2.
1. Given:
Weight on Earth (F1) = 392 N
Mass of the body on Earth (m1) = F1 / g, where g is the acceleration due to gravity on Earth (approximately 9.8 m/s^2)
2. Determine the mass of the body on Earth:
m1 = 392 N / 9.8 m/s^2 = 40 kg
3. Given:
Mass of the new planet (m2) = 2 * mass of Earth (m1)
Radius of the new planet (r2) = 4 * radius of Earth
4. Determine the weight of the body on the new planet (F2):
F2 = G * (m1 * m2) / r2^2
First, let's calculate the mass of the new planet:
Mass of Earth = 5.972 × 10^24 kg (approx.)
Mass of the new planet = 2 * 5.972 × 10^24 kg = 1.1944 × 10^25 kg
Next, let's calculate the radius of the new planet:
Radius of Earth = 6.371 × 10^6 m (approx.)
Radius of the new planet = 4 * 6.371 × 10^6 m = 2.5484 × 10^7 m
Now, we can calculate the weight of the body on the new planet:
F2 = 6.674 × 10^-11 N m^2/kg^2 * (40 kg * 1.1944 × 10^25 kg) / (2.5484 × 10^7 m)^2
Using a calculator, we can compute the value of F2. The weight of the body on the new planet will be the result obtained.
Please note that the answer may result in a very small value, as the radius and mass of the new planet are much larger than Earth.
To find the weight of the body on a different planet, we need to use Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
In this case, we have the weight of the body on the surface of the Earth, which is given as 392N. This weight is caused by the gravitational force between the body and the Earth.
To find the weight of the body on another planet, we can use the equation:
W = (G * m1 * m2) / r^2
Where:
W is the weight of the body
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2 / kg^2)
m1 is the mass of the body
m2 is the mass of the planet
r is the radius of the planet
Let's go step by step:
1. Find the mass of the body.
Since weight is a force, it is measured in Newtons (N). Weight is calculated by multiplying the mass of the object by the acceleration due to gravity. So, we can use the equation:
W = m * g
Rearranging the equation, we get:
m = W / g
Given that the weight of the body on Earth is 392N and the acceleration due to gravity on Earth is approximately 9.8 m/s^2, we can substitute these values to find the mass of the body on Earth.
m = 392N / 9.8 m/s^2
m ≈ 40 kg
Therefore, the mass of the body is approximately 40 kg.
2. Find the mass of the planet.
The problem states that the mass of the planet is double that of the Earth. Assuming the mass of the Earth is approximately 5.972 × 10^24 kg, we can calculate the mass of the planet.
Mass of the planet = 2 * Mass of the Earth
Mass of the planet ≈ 2 * 5.972 × 10^24 kg
Mass of the planet ≈ 1.1944 × 10^25 kg
Therefore, the mass of the planet is approximately 1.1944 × 10^25 kg.
3. Find the radius of the planet.
The problem states that the radius of the planet is four times that of the Earth. Assuming the radius of the Earth is approximately 6,371 km, we can calculate the radius of the planet.
Radius of the planet = 4 * Radius of the Earth
Radius of the planet ≈ 4 * 6,371 km
Radius of the planet ≈ 25,484 km
(Converting km to meters: 1 km = 1000 m)
Radius of the planet ≈ 25,484,000 m
Therefore, the radius of the planet is approximately 25,484,000 m.
4. Calculate the weight of the body on the planet.
Now that we have all the necessary values, we can substitute them into the formula:
W = (G * m1 * m2) / r^2
W = (6.67430 × 10^-11 N m^2 / kg^2 * 40 kg * 1.1944 × 10^25 kg) / (25,484,000 m)^2
Solving this equation will give us the weight of the body on the planet.
W ≈ 115 N
Therefore, the weight of the body on the planet whose mass is double that of the Earth and radius is four times that of the Earth is approximately 115N.
forcegravity=k Mass/r^2
double the mass...
forcegravity=392* 2/(4^2)=392/8 N