A mass 'm' is taken to a planet whose mass is equal to half that of earth and radius is four times that of earth. The mass of the body on this planet will be

The correct answer is m.

To understand this result, we must distinguish between two fundamental physical concepts: mass and weight.

1. Mass:
Mass is a measure of the quantity of matter contained within a body. It is an intrinsic property, meaning it does not change regardless of where the object is located in the universe. Whether the body is on Earth, on a different planet, or in deep space, its mass remains constant.

2. Weight:
Weight is the gravitational force exerted on a body by a planet or celestial body. It is dependent on the local acceleration due to gravity, which is represented by:
$g$
Weight is calculated using the formula:
$W=mg$
While the gravity on the new planet is different from Earth's gravity due to the changes in planetary mass and radius, this difference only affects the weight of the body, not its mass.

Since the question asks for the mass of the body on the planet, and mass is independent of gravity, the mass remains exactly the same as it was on Earth, which is:
$m$