the mass of a body is 50 kg on the surface of the earth.find its weight on the surface of a planet whose mass is double than the mass of the earth and radius is 5 times the radius of the earth

Let g', M' and R' be values for the new planet.

Let g be the acceleration of gravity for Earth, 9.8 m/s^2

g' = G*m'/R'^2 = 2G*Me/(5R2)^2)
= (2/25)G*Me/Re^2 = 0.08 g

Weight = 0.08 M g = 39.2 N

Weight = (0.08)M g =

To find the weight of the body on the surface of the planet, we need to consider two factors: the gravitational force and the mass of the body.

The gravitational force between two objects is given by the equation:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 x 10^-11 N(m/kg)^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects

To compare the weight on the new planet to that on Earth, we need to consider the change in the gravitational force due to the planet's increased mass and increased radius.

Let's calculate the weight of the body on the given planet:

Step 1: Calculate the mass of the planet (m2)
The mass of the given planet is double the mass of the Earth. Since the mass of the Earth is approximately 5.972 × 10^24 kg, the mass of the given planet is 2 * 5.972 × 10^24 kg = 1.1944 × 10^25 kg.

Step 2: Calculate the radius of the planet (r)
The radius of the given planet is 5 times the radius of the Earth. Since the radius of the Earth is approximately 6,371 km, the radius of the given planet would be 5 * 6,371 km = 31,855 km = 31,855,000 meters.

Step 3: Calculate the gravitational force on the planet (F)
Using the equation mentioned above, we can calculate the gravitational force between the body and the given planet.

F = (G * m1 * m2) / r^2

From the question, we know that the mass of the body (m1) is 50 kg.

Plugging the values into the equation:
F = (6.67430 x 10^-11 N(m/kg)^2 * 50 kg * 1.1944 × 10^25 kg) / (31,855,000 m)^2

Calculating this equation will give the weight (gravity) of the body on the surface of the given planet.