Question 355: Gravitation

Question

The mass of a spherical planet is 4 times the mass of the earth, but its radius (R) is same as that of the earth. How much work is done is lifting a body of mass 5 kg through a distance of 2 m on the planet ? (g = 10 ms$$^{-2}$$)

Accepted Answer

To determine the work done in lifting a body of mass 5 kg through a distance of 2 m on the spherical planet with the given conditions, weÃ¢ÂÂll proceed step-by-step.
First, let's establish the gravitational force acting on the body on the planet, specifically the relationship between the gravitational forces on Earth and the planet.
Given:
The mass of the planet is 4 times the mass of Earth.
The radius (R) of the planet is the same as that of Earth.
The gravitational acceleration on Earth, $$g = 10 \, 	ext{m/s}^2$$.
The gravitational force at the surface of a planet is given by Newton's law of gravitation:
$$ F = \frac{G M m}{R^2} $$
where:
$ G $ is the gravitational constant,
$ M $ is the mass of the planet,
$ m $ is the mass of the object, and
$ R $ is the radius of the planet.
Since the planet has 4 times the mass of Earth and the same radius, the gravitational acceleration $ g' $ on the planet can be written as:
$$ g' = \frac{G \cdot (4 M_{	ext{Earth}})}{R^2} $$
Comparing with Earth's gravity:
$$ g_{	ext{Earth}} = \frac{G M_{	ext{Earth}}}{R^2} $$
Thus,
$$ g' = 4 g_{	ext{Earth}} $$
Given $$ g_{	ext{Earth}} = 10 \, 	ext{m/s}^2 $$, we have:
$$ g' = 4 	imes 10 \, 	ext{m/s}^2 = 40 \, 	ext{m/s}^2 $$
Now, the work done in lifting a body through a vertical distance $ h $ is given by:
$$ W = m g' h $$
Substituting the given values:
$ m = 5 \, 	ext{kg} $
$ g' = 40 \, 	ext{m/s}^2 $
$ h = 2 \, 	ext{m} $
$$ W = 5 \, 	ext{kg} 	imes 40 \, 	ext{m/s}^2 	imes 2 \, 	ext{m} = 400 \, 	ext{J} $$
Therefore, the work done is:
400 J
The correct answer is Option A: 400 J.

Answer

400 J

Answer

200 J

Answer

800 J

Answer

300 J

Gravitation

The mass of a spherical planet is 4 times the mass of the earth, but its radius (R) is same as that of the earth. How much work is done is lifting a body of mass 5 kg through a distance of 2 m on the planet ? (g = 10 ms$^{-2}$)

Choose the correct answer: