Newton's law of universal gravitation Knowledge-Based Download PDF

Questions

1. 1.

   At what altitude $h$ above the surface of a spherical planet of radius $R$ is the gravitational force exerted by the planet on an object equal to one-ninth of its surface weight?

   • A) $h = 9R$
   • B) $h = 3R$
   • C) $h = 2R$
   • D) $h = \frac{1}{3}R$
2. 2.

   Two satellites, $P$ and $Q$, travel in circular orbits around a planet with orbital radii $R$ and $4R$, respectively. If satellite $P$ has an orbital period of $T$, what is the orbital period of satellite $Q$?

   • A) $2T$
   • B) $4T$
   • C) $16T$
   • D) $8T$
3. 3.

   A uniform spherical planet has the same average mass density as Earth but twice the radius of Earth. If the magnitude of the gravitational acceleration at the surface of Earth is $g$, what is the magnitude of the gravitational acceleration at the surface of this planet?

   • A) $2g$
   • B) $4g$
   • C) $\frac{1}{2}g$
   • D) $\frac{1}{4}g$
4. 4.

   A satellite of mass $m$ moves in a circular orbit of radius $r$ around a planet of mass $M$. What is the orbital speed $v$ of the satellite in terms of the universal gravitational constant $G$, $M$, and $r$?

   • A) $v = \sqrt{\frac{GM}{r^2}}$
   • B) $v = \frac{GM}{r}$
   • C) $v = \sqrt{\frac{GMm}{r}}$
   • D) $v = \sqrt{\frac{GM}{r}}$
5. 5.

   A total mass $M$ is divided into two point masses, $m$ and $M - m$, which are placed at a fixed separation distance. What value of $m$ maximizes the magnitude of the mutual gravitational force between the two masses?

   • A) $m = \frac{M}{4}$
   • B) $m = \frac{M}{2}$
   • C) $m = \frac{M}{3}$
   • D) $m = \frac{2M}{3}$
6. 6.

   Two identical particles of mass $m$ are separated by a distance $d$ and exert a mutual gravitational force of magnitude $F$ on each other. If a third identical particle is placed so that the three particles form an equilateral triangle of side length $d$, what is the magnitude of the net gravitational force on any one of the particles?

   • A) $\sqrt{3}F$
   • B) $2F$
   • C) $\sqrt{2}F$
   • D) $\frac{\sqrt{3}}{2}F$
7. 7.

   Two point masses, $4M$ and $M$, are held at a fixed separation distance $L$. At what distance from the mass $4M$ along the line connecting them will a third point mass experience zero net gravitational force?

   • A) $\frac{1}{3}L$
   • B) $\frac{1}{2}L$
   • C) $\frac{2}{3}L$
   • D) $\frac{4}{5}L$
8. 8.

   Two identical uniform spheres, each of mass $m$ and radius $R$, are in contact with each other in deep space. What is the magnitude of the gravitational force exerted by one sphere on the other?

   • A) $\frac{G m^2}{R^2}$
   • B) $\frac{G m^2}{4R^2}$
   • C) $\frac{G m^2}{2R^2}$
   • D) $\frac{2G m^2}{R^2}$
9. 9.

   Two isolated spherical masses, $X$ with mass $4m$ and $Y$ with mass $m$, interact solely through their mutual gravitational attraction. Which statement correctly relates the magnitude of the gravitational force $F_{XY}$ exerted by $X$ on $Y$ to $F_{YX}$ exerted by $Y$ on $X$, as well as their resulting accelerations $a_X$ and $a_Y$?

   • A) $F_{XY} = 4F_{YX}$ and $a_Y = a_X$
   • B) $F_{XY} = F_{YX}$ and $a_Y = 4a_X$
   • C) $F_{XY} = F_{YX}$ and $a_X = 4a_Y$
   • D) $F_{XY} = 4F_{YX}$ and $a_Y = 4a_X$
10. 10.

    Two spherical masses separated by a center-to-center distance $r$ exert an attractive gravitational force of magnitude $F$ on each other. If the distance between their centers is tripled while one mass is doubled and the other remains unchanged, what is the magnitude of the new gravitational force?

    • A) $\frac{2}{3}F$
    • B) $\frac{1}{3}F$
    • C) $\frac{2}{9}F$
    • D) $\frac{4}{9}F$