Question

Some comparisons between Earth and a heavenly body are as follows: Mass of Earth= 10 times the mass of heavenly body Radius of Earth=- 2 times radius of heavenly body If the weight of 1kg of water is 10 N on Earth, Calculate the weight of 10 kg of water on heavenly body.​

Answer 1

We can use the formula for gravitational force to calculate the weight of 10 kg of water on the heavenly body:

F = G (m1m2)/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 their centers.

First, let's find the mass and radius of the heavenly body in terms of Earth's values:

Mass of heavenly body = (1/10) * Mass of Earth
Radius of heavenly body = (1/2) * Radius of Earth

Now we can substitute these values into the gravitational force formula and solve for the weight of 10 kg of water on the heavenly body:

F = G [(10 kg) * (1/10) * (Mass of Earth)] / [(1/2 * Radius of Earth)^2]

F = G [(10 kg) * (1/10) * (10 * weight of 1kg of water)] / [(1/2 * radius of Earth)^2]

F = G * weight of 1kg of water * 50

F = (6.674 × 10^-11 N m^2/kg^2) * (10 N) * 50

F = 3.337 × 10^-8 N

So the weight of 10 kg of water on the heavenly body is 3.337 × 10^-8 N.

Answer 2

Let's assume that the heavenly body has a mass of m and a radius of r. According to the given information:

Mass of Earth = 10 times the mass of heavenly body

Therefore, the mass of the heavenly body = 1/10 times the mass of Earth

m = (1/10) * M

Radius of Earth = -2 times radius of heavenly body

Therefore, the radius of the heavenly body = -1/2 times the radius of Earth

r = (-1/2) * R

Weight of 1 kg of water on Earth = 10 N

This means that the gravitational acceleration on Earth is g = 10 m/s^2

To calculate the weight of 10 kg of water on the heavenly body, we can use the formula for weight:

weight = mass * gravitational acceleration

The mass of 10 kg of water is 10 kg, and the gravitational acceleration on the heavenly body can be calculated using the formula:

g' = G * m / r^2

where G is the gravitational constant (6.67 x 10^-11 N*m^2/kg^2).

Substituting the values, we get:

g' = G * m / r^2

g' = 6.67 x 10^-11 * (1/10) * M / ((-1/2) * R)^2

g' = 2.688*10^-11 * M / R^2

Now, we can calculate the weight of 10 kg of water on the heavenly body:

weight = mass * gravitational acceleration

weight = 10 * (2.688*10^-11 * M / R^2)

weight = 2.668 x 10^-10* M / R^2

Therefore, the weight of 10 kg of water on the heavenly body is 2.668 x 10^-10 times the mass of the heavenly body divided by the square of its radius.