Consider a planet in space whose mass is twice that of earth and radius is thrice that of earth what will be the weight of a body on this planet if its weight on the earth is 900N ??

To calculate the weight of a body on the given planet, we need to consider the gravitational force acting on it. The weight of an object can be determined using the formula:

Weight = mass * gravitational acceleration

Since the mass of the body remains constant, we only need to find the gravitational acceleration on the new planet.

The formula for gravitational acceleration is:

g = G * (m1 / r^2)

Where:
g is the gravitational acceleration
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
m1 is the mass of the planet
r is the radius of the planet

First, let's compare the masses and radii of the new planet and Earth:

Mass of the new planet = 2 * Mass of Earth
Radius of the new planet = 3 * Radius of Earth

Next, let's calculate the gravitational acceleration on the new planet:

g_new = G * (mass_new_planet / radius_new_planet^2)

Using the given information about Earth's weight, which is 900N, and the gravitational acceleration on Earth, which is approximately 9.8 m/s^2, we can solve for the mass of the body using the formula:

Weight_on_Earth = mass * gravitational acceleration_on_Earth

Rearranging the equation, we have:

mass = Weight_on_Earth / gravitational acceleration_on_Earth

Now that we have the mass of the body, we can calculate the gravitational acceleration on the new planet using the formula mentioned earlier:

g_new = G * (mass_new_planet / radius_new_planet^2)

Finally, we can find the weight of the body on the new planet using the formula:

Weight_on_new_planet = mass * g_new

Let's now calculate the weight of the body on the new planet:

1. Calculate the mass of the body:
mass = Weight_on_Earth / gravitational acceleration_on_Earth

2. Calculate the gravitational acceleration on the new planet:
g_new = G * (mass_new_planet / radius_new_planet^2)

3. Calculate the weight of the body on the new planet:
Weight_on_new_planet = mass * g_new

Substituting the values given in the problem:

Mass of Earth = m1
Radius of Earth = r
Mass of the body on Earth = 900N

mass_new_planet = 2 * mass_earth
radius_new_planet = 3 * radius_earth

g_new = G * (mass_new_planet / radius_new_planet^2)
Weight_on_new_planet = mass * g_new

Using the calculations and formulas above, you can find the weight of the body on the given planet.

(This must be math...)

F = G Mm/r^2
If M is doubled then F will be doubled.
If r is tripled then F is reduced to 1/9
The overall effect is 2 x 1/9 = 2 / 9
so W(on Earth) / w (on planet) = 2 / 9
W(on Earth) = 900 x 2 / 9 = 200 N