Gravitational field strength Knowledge-Based Practice

Questions

1. 1.

   Which statement correctly describes the direction of the gravitational field strength vector at any point in the region surrounding an isolated point mass?

   • A) It points tangentially along concentric circles centered on the mass.
   • B) It points radially outward, directed away from the mass.
   • C) It has no direction because gravitational field strength is a scalar quantity.
   • D) It points radially inward, directed toward the mass.
2. 2.

   Three identical point masses, each of mass $M$, are fixed at the vertices of an equilateral triangle, each at a distance $r$ from the centroid. If one of the masses is removed, what is the magnitude of the net gravitational field strength at the centroid of the triangle?

   • A) $\frac{GM}{r^2}$
   • B) 0
   • C) $\frac{2GM}{r^2}$
   • D) $\frac{\sqrt{3}GM}{r^2}$
3. 3.

   A satellite travels in a circular orbit of radius $r$ around a planet where the magnitude of the gravitational field strength is $g$. What is the orbital speed $v$ of the satellite?

   • A) $v = \sqrt{gr}$
   • B) $v = gr$
   • C) $v = \frac{g}{r}$
   • D) $v = \sqrt{\frac{g}{r}}$
4. 4.

   A small test mass $m$ experiences a gravitational force of magnitude $F$ when placed at a fixed point $P$ in a gravitational field. If the test mass is replaced at point $P$ by a new test mass of $2m$, what is the magnitude of the gravitational field strength at point $P$?

   • A) $\frac{F}{m}$
   • B) $\frac{2F}{m}$
   • C) $\frac{F}{2m}$
   • D) $\frac{4F}{m}$
5. 5.

   A uniform spherical planet has a radius $R$ and a gravitational field strength of magnitude $g$ at its surface. Which expression represents the mass of the planet in terms of $g$, $R$, and the universal gravitational constant $G$?

   • A) $\frac{g R}{G}$
   • B) $\frac{g R^2}{G}$
   • C) $\frac{G R^2}{g}$
   • D) $\frac{g^2 R}{G}$
6. 6.

   A satellite travels in a circular orbit of radius $r$ around a planet with an orbital period $T$. What is the magnitude of the gravitational field strength of the planet at the radius of the satellite's orbit?

   • A) $\frac{4\pi^2 r}{T^2}$
   • B) $\frac{4\pi^2 r^2}{T^2}$
   • C) $\frac{2\pi r}{T}$
   • D) $\frac{4\pi^2 r^3}{T^2}$
7. 7.

   Two isolated spherical bodies with masses $M$ and $4M$ are separated by a center-to-center distance $d$. At what distance from the center of mass $M$, along the line connecting their centers, is the net gravitational field strength equal to zero?

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

   Two uniform spherical planets, A and B, have the same mean density. If the radius of planet A is three times the radius of planet B, what is the ratio of the gravitational field strength at the surface of planet A to that at the surface of planet B, $\frac{g_A}{g_B}$?

   • A) 3
   • B) 9
   • C) $\frac{1}{3}$
   • D) 27
9. 9.

   Planet X has twice the mass and twice the radius of Planet Y. If the gravitational field strength at the surface of Planet Y is $g$, what is the gravitational field strength at the surface of Planet X?

   • A) $\frac{1}{2}g$
   • B) $g$
   • C) $2g$
   • D) $4g$
10. 10.

    A uniform spherical planet has a radius of $R$ and a gravitational field strength of $g$ at its surface. What is the gravitational field strength at an altitude of $R$ above the planet's surface?

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

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