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

(D) The weight of the passenger is the net gravitational force acting on them. Let $M_e$ and $M_m$ be the masses of Earth and Mars,and $R_e$ and $R_m$

Vedclass · Accepted Answer

$D$

Vedclass · Answer

(D) The weight of the passenger is the net gravitational force acting on them. Let $M_e$ and $M_m$ be the masses of Earth and Mars,and $R_e$ and $R_m$ be their radii. The gravitational force $F$ at a distance $x$ from Earth along the path is given by $F = |F_e - F_m| = |\frac{G M_e m}{x^2} - \frac{G M_m m}{(d-x)^2}|$,where $d$ is the distance between Earth and Mars.At the surface of Earth $(x = R_e)$,the weight is $W_e = m g_e = 60 	imes 10 = 600 \, N$.At the surface of Mars $(x = d - R_m)$,the weight is $W_m = m g_m = 60 	imes 4 = 240 \, N$.As the spaceship moves from Earth to Mars,the gravitational pull of Earth decreases and the gravitational pull of Mars increases. At some point between the two planets,the gravitational forces from Earth and Mars will be equal in magnitude,making the net gravitational force (weight) zero.Since the spaceship moves with constant velocity,the distance $x$ is proportional to time $t$. Therefore,the graph of weight versus time must decrease from $600 \, N$,reach $0 \, N$ at some intermediate time,and then increase to $240 \, N$ at the arrival time $t_0$. Curve $D$ is the only one that shows the weight becoming zero and then increasing to $240 \, N$.

Similar Questions

Which one of the following plots represents the variation of gravitational field on a particle with distance $r$ due to a thin spherical shell of radius $R$? ($r$ is measured from the centre of the spherical shell)

Select the correct choice$(s)$:

$A$ particle of mass $M$ is at a distance $a$ from the surface of a thin spherical shell of equal mass $M$ and radius $a$. Which of the following statements is correct regarding the gravitational field and potential inside the shell?

Vedclass Test Series

Exam Paper Generator

Online Exam Module