Newton's law of universal gravitation Knowledge-Based Practice

Questions

1. 1.

   What is the unit of the universal gravitational constant, $G$, when expressed in SI base units?

   • A) $\text{kg}^{-1}\cdot\text{m}^2\cdot\text{s}^{-2}$
   • B) $\text{kg}^{-1}\cdot\text{m}^3\cdot\text{s}^{-2}$
   • C) $\text{kg}^{-2}\cdot\text{m}^3\cdot\text{s}^{-2}$
   • D) $\text{kg}\cdot\text{m}^3\cdot\text{s}^{-2}$
2. 2.

   Three identical point masses, each of mass $m$, are located at the vertices of an equilateral triangle with side length $L$. What is the magnitude of the net gravitational force exerted on any one of the masses?

   • A) $\sqrt{3}\frac{Gm^2}{L^2}$
   • B) $2\frac{Gm^2}{L^2}$
   • C) $\frac{Gm^2}{L^2}$
   • D) $\frac{\sqrt{3}}{2}\frac{Gm^2}{L^2}$
3. 3.

   Two identical uniform solid spheres of radius $R$ made of the same material are placed in contact with each other, exerting a mutual gravitational force of magnitude $F$. If they are replaced by two identical spheres of the same material each having radius $2R$ placed in contact, what is the magnitude of the gravitational force between them?

   • A) $4F$
   • B) $16F$
   • C) $8F$
   • D) $64F$
4. 4.

   Three identical point particles, each of mass $m$, are placed along a straight line such that adjacent particles are separated by a distance $d$. What is the magnitude of the net gravitational force exerted on one of the end particles?

   • A) $\frac{3Gm^2}{4d^2}$
   • B) $\frac{5Gm^2}{4d^2}$
   • C) $\frac{2Gm^2}{d^2}$
   • D) $\frac{9Gm^2}{4d^2}$
5. 5.

   Two stationary spherical masses, $M$ and $4M$, are separated by a center-to-center distance $d$. At what distance from the mass $M$ along the line connecting their centers is the net gravitational force on a small test mass equal to zero?

   • A) $d/3$
   • B) $d/4$
   • C) $d/5$
   • D) $d/2$
6. 6.

   Two point particles separated by a distance $r$ exert an attractive gravitational force of magnitude $F$ on each other. If the separation distance between the particles is reduced to one-third of its initial value without changing their masses, what is the magnitude of the new gravitational force?

   • A) $\frac{F}{9}$
   • B) $3F$
   • C) $9F$
   • D) $27F$
7. 7.

   A satellite has a weight $W$ on the surface of a uniform spherical planet of radius $R$. What is the magnitude of the gravitational force exerted on the satellite when it is at an altitude equal to $R$ above the planet's surface?

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

   Two identical spherical masses separated by a center-to-center distance $r$ exert an attractive gravitational force $F$ on each other. If each mass is increased to three times its initial value, what new center-to-center separation is required to keep the gravitational force equal to $F$?

   • A) $\frac{1}{3}r$
   • B) $3r$
   • C) $9r$
   • D) $\sqrt{3}r$
9. 9.

   A small probe of mass $m$ is situated in deep space at a distance $r$ from a massive planet of mass $1\,000m$. How does the magnitude of the gravitational force exerted by the probe on the planet compare with the magnitude of the gravitational force exerted by the planet on the probe?

   • A) It is equal to the force exerted by the planet on the probe.
   • B) It is $1\,000$ times smaller than the force exerted by the planet on the probe.
   • C) It is $1\,000$ times greater than the force exerted by the planet on the probe.
   • D) It is $1\,000\,000$ times smaller than the force exerted by the planet on the probe.
10. 10.

    Two uniform spherical bodies separated by a center-to-center distance $r$ exert a gravitational attractive force of magnitude $F$ on each other. If the mass of one body is doubled while the center-to-center distance is also doubled, what is the magnitude of the new gravitational force between them?

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

Answers and step-by-step solutions appear after you finish the test.