Gravitational field strength Knowledge-Based Download PDF

Questions

1. 1.

   Two point masses, each of mass $M$, are held at two vertices of an equilateral triangle of side length $a$. What is the magnitude of the net gravitational field strength at the third vertex?

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

   A spherical planet of radius $R$ produces a gravitational field strength of magnitude $g$ at an external point located at a distance of $2R$ from its center. If the planet contracts uniformly to a radius of $0.5R$ while maintaining the same total mass, what is the magnitude of the gravitational field strength at that same point?

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

   A spherical planet has a radius $R$, and the gravitational field strength at its surface is $g$. Neglecting atmospheric drag, what is the orbital speed of a satellite in a circular orbit just above the planet's surface?

   • A) $gR$
   • B) $\sqrt{2gR}$
   • C) $\frac{g}{R}$
   • D) $\sqrt{gR}$
4. 4.

   Two spherical planets, X and Y, have the same uniform mass density. If the radius of planet X is twice the radius of planet Y, what is the ratio of the gravitational field strength at the surface of planet X to that at the surface of planet Y?

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

   A hypothetical planet is modeled as a solid sphere of uniform mass density and radius $R$. If the gravitational field strength at its surface is $g$, what is the magnitude of the gravitational field strength at a distance of $R / 3$ from the center of the planet?

   • A) $g / 9$
   • B) $g / 3$
   • C) $g$
   • D) $3g$
6. 6.

   A small test mass $m$ placed at a point in a gravitational field experiences a gravitational force of magnitude $F$. If the test mass is replaced by a mass of $3m$ at the exact same location, what is the magnitude of the gravitational field strength at that point?

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

   A satellite of mass $m$ orbits a planet in a circular path of radius $r$ with an orbital period $T$. What is the magnitude of the planet's gravitational field strength at this orbital radius?

   • A) $\frac{2\pi r}{T}$
   • B) $\frac{2\pi r}{T^2}$
   • C) $\frac{4\pi^2 r}{T^2}$
   • D) $\frac{4\pi^2 r^2}{T^2}$
8. 8.

   At what altitude above the surface of a uniform spherical planet of radius $R$ does the gravitational field strength drop to one-ninth of its value at the surface?

   • A) $R$
   • B) $8R$
   • C) $3R$
   • D) $2R$
9. 9.

   Two isolated point masses, $M$ and $4M$, are fixed at a distance $d$ apart in deep space. At what distance from mass $M$, along the line connecting the two masses, is the net gravitational field strength equal to zero?

   • A) $d/5$
   • B) $d/4$
   • C) $d/2$
   • D) $d/3$
10. 10.

    A hypothetical spherical planet has three times the mass and twice the radius of Earth. If the gravitational field strength at the surface of Earth is $g$, what is the gravitational field strength at the surface of this planet?

    • A) $\frac{3}{2}g$
    • B) $\frac{3}{4}g$
    • C) $\frac{9}{4}g$
    • D) $\frac{3}{8}g$