A $90 \mathrm{~kg}$ body placed at $2 \mathrm{R}$ distance from surface of earth experiences gravitational pull of :

($\mathrm{R}=$ Radius of earth, $\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$)

<p>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:</p> <p>$F = \frac{G M m}{r^2}$</p> <p>Where:</p> <ul> <li>$G$ is the gravitational constant ($6.674 \times 10^{-11} \text{Nm}^2/\text{kg}^2$)</li> <li>$M$ is the mass of the Earth (approximately $5.972 \times 10^{24} \text{kg}$)</li> <li>$m$ is the mass of the object</li> <li>$r$ is the distance from the center of the Earth to the object</li> </ul> <p>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 $3R$.</p> <p>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 $g = 10 \text{m/s}^2$ and the mass of the body $m = 90 \text{kg}$, we get:</p> <p>$F_{earth} = 90 \text{kg} \cdot 10 \text{m/s}^2 = 900 \text{N}$</p> <p>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.</p> <p>Therefore, the gravitational pull $F_{2R}$ on the body when placed at $2R$ from the Earth's surface is:</p> <p>$F_{2R} = \frac{F_{earth}}{9} = \frac{900 \text{N}}{9} = 100 \text{N}$</p> <p>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:</p> <p>Option C: 100 N</p>