Suppose the acceleration due to gravity at th | vedclass

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

Question

(C) Let $M_e$ and $R_e$ be the mass and radius of the earth, and $M_m$ and $R_m$ be the mass and radius of the moon. Let $D$ be the distance between t

Vedclass · Accepted Answer

$C$

Vedclass · Answer

(C) Let $M_e$ and $R_e$ be the mass and radius of the earth, and $M_m$ and $R_m$ be the mass and radius of the moon. Let $D$ be the distance between the centers of the earth and the moon.If the spaceship is at a distance $x$ from the center of the earth, the net gravitational force $F$ on the passenger of mass $M$ is given by $F = \frac{G M_e M}{x^2} - \frac{G M_m M}{(D-x)^2}$.Since the spaceship moves with constant velocity $v$, $x = vt$. Thus, $F(t) = G M \left( \frac{M_e}{(vt)^2} - \frac{M_m}{(D-vt)^2} \right)$.At $t=0$ (on Earth's surface), $F = Mg$. At $t=t_m$ (on Moon's surface), $F = Mg'$.Between the Earth and the Moon, there exists a point (neutral point) where the gravitational pull of the Earth and the Moon cancel each other out, meaning $F=0$. This occurs at some time $t$ between $0$ and $t_m$.Curve $C$ is the only one that shows the force decreasing from $Mg$, reaching zero at the neutral point, and then increasing to $Mg'$ at the moon's surface.

Similar Questions

Which of the following symptoms is likely to afflict an astronaut in space? $(a)$ Swollen feet,$(b)$ Swollen face,$(c)$ Headache,$(d)$ Orientational problem.

Four identical particles of mass $M$ are located at the corners of a square of side $a$. What should be their speed if each of them revolves under the influence of the others' gravitational field in a circular orbit circumscribing the square?

$A$ particle of mass $m$ starts from rest at a distance $R$ from the centre and along the axis of a fixed ring of radius $R$ and mass $M$. Its velocity at the centre of the ring is:

$A$ satellite of mass $m$ is at a distance of $a$ from a star of mass $M$. The speed of the satellite is $u$. Suppose the law of universal gravity is $F = -G \frac{Mm}{r^{2.1}}$ instead of $F = -G \frac{Mm}{r^2}$. Find the speed of the satellite when it is at a distance $b$ from the star.

Vedclass Test Series

Exam Paper Generator

Online Exam Module