A rocket is fired from the Earth towards the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $M_s = 2 	imes 10^{30} \; kg$ be the mass of the Sun and $M_e = 6 	imes 10^{24} \; kg$ be the mass of the Earth. The distance between them i

Vedclass · Accepted Answer

$2.59 	imes 10^{8} \; m$

Vedclass · Answer

(D) Let $M_s = 2 	imes 10^{30} \; kg$ be the mass of the Sun and $M_e = 6 	imes 10^{24} \; kg$ be the mass of the Earth. The distance between them is $r = 1.5 	imes 10^{11} \; m$.Let $x$ be the distance from the Earth's centre where the net gravitational force on the rocket of mass $m$ is zero.At this point,the gravitational pull of the Earth equals the gravitational pull of the Sun:$\frac{G M_e m}{x^2} = \frac{G M_s m}{(r - x)^2}$$\frac{M_e}{x^2} = \frac{M_s}{(r - x)^2}$Taking the square root on both sides:$\frac{\sqrt{M_e}}{x} = \frac{\sqrt{M_s}}{r - x}$$\frac{r - x}{x} = \sqrt{\frac{M_s}{M_e}}$$\frac{r}{x} - 1 = \sqrt{\frac{2 	imes 10^{30}}{6 	imes 10^{24}}} = \sqrt{\frac{1}{3} 	imes 10^6} = \frac{1000}{\sqrt{3}} \approx 577.35$$\frac{r}{x} = 578.35$$x = \frac{1.5 	imes 10^{11}}{578.35} \approx 2.59 	imes 10^8 \; m$.

Similar Questions

Two solid spheres each of radius $R$ made of the same material are placed in contact with each other. If the gravitational force acting between them is $F$,then:

Two metallic spheres each of mass $M$ are suspended by two strings each of length $L$. The distance between the upper ends of the strings is $L$. The angle which the strings will make with the vertical due to the mutual attraction of the spheres is

The atmosphere is held to the earth by

If two identical spherical bodies of same material and dimensions are kept in contact,the gravitational force between them is proportional to $R^{x}$,where $x$ is a non-zero integer. [Given: $R$ is the radius of each spherical body]

The gravitational force between two identical uniform solid gold spheres of radius $r$ placed in contact is proportional to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module