The gravity of a planet depends just on its mass, not on its size. The density of planets is quiet different. Rocky planets (Mercury, Venus, Earth and Mars) have a much higher density than the gas giants (Jupiter, Saturn, Uranus and Neptune). However, the gas giants have higher masses because of their different formation (see, e.g., https://exoplanets.nasa.gov/faq/43/how-do-planets-form/). Each planet has its individual density. As an example, Neptune is the fourth-largest planet in the Solar System by diameter but the third-most-massive planet because it is the densest of the giant planets.

Dr Wolfgang R Dick thank you for your contribution to the discussion

Yes, it can be possible, and I can give you a solid example that exists in real life, and that too, in our solar system. Uranus is about 4 times wider than the Earth, and is 14x the mass. Yet, Uranus has the same gravity as Venus, a meagre 8.87 m/s2. Uranus has about 10% lower gravity than Earth's. No, a planet twice the size of Earth would not necessarily have twice the gravity. It would depend on the mass and density of that planet. If its mass is also roughly twice that of Earth, then the gravitational force on its surface would be greater than twice Earth's gravity. A planet's size and mass determines its gravitational pull. A planet's mass and size determines how strong its gravitational pull is. Models can help us experiment with the motions of objects in space, which are determined by the gravitational pull between them.The gravity of a planet, or other body, is proportional to its mass. The density of the Earth is about 5.51 g/ cm3. A planet with double the volume of the Earth would have to have half the density to have the same mass and hence the same gravity. Now 2.75 g/ cm3 is about the density of some of the lighter rocks. If its gravity is too strong our blood will be pulled down into our legs, our bones might break, and we could even be pinned helplessly to the ground. Finding the gravitational limit of the human body is something that's better done before we land on a massive new planet.If Earth's diameter were doubled to about 16,000 miles, the planet's mass would increase eight times, and the force of gravity on the planet would be twice as strong. If you could stand on the cloud tops of Jupiter, you would experience 2.5 times the gravity that you experience on Earth. Then you'd fall to your death, because it's a gas planet, made of hydrogen, the lightest element in the Universe. Therefore, if a planet has same radius as that of earth but double the mass of earth, it will have twice the gravity. But if this planet is also bigger than earth, it won't be double as larger radius will make its gravity lower. The bigger the mass, the stronger the gravity this is direct and unavoidable. If we assume that the density of the Earth stays the same, then doubling the radius increases the planet's mass eight-fold. Surface gravity is now doubled, so most plants and trees promptly fall over.The bigger the size for a given mass, the smaller the gravity, since you are farther from the center of mass. A smaller planet can have stronger gravity if its density is higher. A planet only half the diameter of Earth could have a similar gravity of its density was twice that of Earth. Anything with mass also has gravity. The more mass something has (Earth has a mass of 6.6 sextillion tons), the higher the force of gravity that it exerts on the objects around it. The force of gravity also increases or decreases with distance. The closer the objects are, the stronger the force of gravity will be.

As per Newton's universal law of gravitation, The force of attraction F between any two bodies having mass M and m is given by the equation

F = G (Mm)/r2

where G is Universal Gravitation Constant and r is the radial distance between the two masses.

If the planet is double the size in mass, the force will be doubled.

If the planet is double in terms of radius, the force will be four times less.

If the planet is double the size in terms of mass and also double the size in terms of radius, the net force will be halved.

In the question, Dr. Rk Naresh the word double is ambiguous.

The equation can also be written as F = mg

where g is acceleration due to gravity that can be derived from the formula. If g increases, the objects would fall faster when dropped from a height. An object when thrown above, increased g will shorten its trajectory in terms of height.

Hope this helps.

Dr Atul Kumar Kuthiala thank you for your contribution to the discussion

If Earth's diameter were doubled to about 16,000 miles, the planet's mass would increase eight times, and the force of gravity on the planet would be twice as strong. The gravity of a planet, or other body, is proportional to its mass. The density of the Earth is about 5.51 g/ cm3 . A planet with double the volume of the Earth would have to have half the density to have the same mass and hence the same gravity. Now 2.75 g/ cm3 is about the density of some of the lighter rocks. The bigger the mass, the stronger the gravity. This is direct and unavoidable. The bigger the size for a given mass, the smaller the gravity, since you are farther from the center of mass (the center of the planet). Therefore, if a planet has same radius as that of earth but double the mass of earth, it will have twice the gravity. But if this planet is also bigger than earth (that is it has a larger radius), it won't be double as larger radius will make it's gravity lower. It can be possible, and I can give you a solid example that exists in real life, and that too, in our solar system. Uranus is about 4 times wider than the Earth, and is 14x the mass. Yet, Uranus has the same gravity as Venus, a meagre 8.87 m/s2. Uranus has about 10% lower gravity than Earth's. The gravity on Jupiter is greater than the gravity on Earth because Jupiter is more massive. Although Jupiter is a great deal larger in size, its surface gravity is just 2.4 times that of the surface gravity of Earth. This is because Jupiter is mostly made up of gases. If Earth were twice its size, you'd be heavier, because the force of gravity increases as the planet's density and radius increase. It would take more energy to resist gravitational pull, so the structures we have today wouldn't be strong enough to stand as tall as they do now. If its gravity is too strong our blood will be pulled down into our legs, our bones might break, and we could even be pinned helplessly to the ground. Finding the gravitational limit of the human body is something that's better done before we land on a massive new planet.