the weight of the body on the surface of earth is 392N what will be the weight of this body in another body whose mass is double of earth mass and radius is fourth multiple of earth radius?
F=Mm/r^2
so double M, r by 4
2/64=1/32
Mother Teresa memorial
500
To find the weight of a body on another celestial body, we need to use the universal law of gravitation. The formula is as follows:
\[ F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}} \]
where:
- F is the gravitational force between two bodies,
- G is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two bodies,
- r is the distance between the centers of the two bodies.
In this case, we want to find the weight of the body on another celestial body. Since weight is the force exerted by gravity on an object, we can use the above formula to find it.
Let's break down the problem step by step:
Step 1: Find the mass and radius of the Earth.
The mass of the Earth is approximately \( 5.972 \times 10^{24} \) kg, and the radius of the Earth is approximately \( 6.371 \times 10^6 \) meters.
Step 2: Determine the mass and radius of the other celestial body.
You mentioned that the mass of the other body is double the mass of the Earth, so the mass of the other body would be \( 2 \times 5.972 \times 10^{24} \) kg.
Similarly, the radius of the other body is four times the radius of the Earth, so the radius would be \( 4 \times 6.371 \times 10^6 \) meters.
Step 3: Calculate the weight of the body on the other celestial body.
Using the formula for the gravitational force, we can calculate the weight as follows:
\[ F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}} \]
Given that \( F \) (the weight on Earth) is 392 N, we can rearrange the formula to solve for \( F' \) (the weight on the other body):
\[ F' = \left( \frac{{m_2}}{{m_1}} \right) \cdot \left( \frac{{r_2}}{{r_1}} \right)^2 \cdot F \]
Substituting the values, we can calculate \( F' \).
Please note that the value of the gravitational constant (G) is approximately \( 6.6743 \times 10^{-11} \) N m\(^2\)/kg\(^2\).