Question 85: Gravitation

Question

A $$90 \mathrm{~kg}$$ body placed at $$2 \mathrm{R}$$ distance from surface of earth experiences gravitational pull of :
($$\mathrm{R}=$$ Radius of earth, $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$)

Accepted Answer

The gravitational force $$F$$ that an object of mass $$m$$ placed at a distance $$r$$ (from the center of Earth) experiences can be calculated using the universal law of gravitation, given by:
$$F = \frac{G M m}{r^2}$$
Where:
$$G$$ is the gravitational constant ($$6.674 	imes 10^{-11} 	ext{Nm}^2/	ext{kg}^2$$)
$$M$$ is the mass of the Earth (approximately $$5.972 	imes 10^{24} 	ext{kg}$$)
$$m$$ is the mass of the object
$$r$$ is the distance from the center of the Earth to the object
However, when the object is at a distance $$2R$$ from the surface of the Earth, the total distance from the center of the Earth $$r'$$ becomes $$R + 2R = 3R$$. This is because the radius of the Earth $$R$$ is the distance from the Earth's center to its surface, so if the object is $$2R$$ above the surface, the total distance from the center is $$3R$$.
At the surface of the Earth, the gravitational force ($$F_{earth}$$) that acts on an object is given by its weight, which can be calculated using the formula $$F_{earth} = m \cdot g$$, where $$g$$ is the acceleration due to gravity on the surface of the Earth. Given that $$g = 10 	ext{m/s}^2$$ and the mass of the body $$m = 90 	ext{kg}$$, we get:
$$F_{earth} = 90 	ext{kg} \cdot 10 	ext{m/s}^2 = 900 	ext{N}$$
To find the gravitational pull at a distance $$2R$$ from the Earth's surface, we use the fact that gravitational force varies inversely as the square of the distance from the center of the Earth. Since the distance triples ($$3R$$ from $$R$$), the gravitational force becomes $$\frac{1}{3^2} = \frac{1}{9}$$ of the force at the surface.
Therefore, the gravitational pull $$F_{2R}$$ on the body when placed at $$2R$$ from the Earth's surface is:
$$F_{2R} = \frac{F_{earth}}{9} = \frac{900 	ext{N}}{9} = 100 	ext{N}$$
Thus, the gravitational pull on the body when it is placed at a distance of $$2R$$ from the Earth's surface is 100 N. So, the correct option is:
Option C: 100 N

Answer

300 N

Answer

225 N

Answer

100 N

Answer

120 N

Gravitation

A $90 \mathrm{~kg} body placed at 2 \mathrm{R} distance from surface of earth experiences gravitational pull of : (\mathrm{R}= Radius of earth, \mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$)

Choose the correct answer: