Looking for classes? Ksquare Career Institute, Bengaluru →
Gravitational potential
Appears in
Concepts tested here
- Potential inside a shell 2
- Geometric series
All Questions
2013 NEET 1 question
-
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m, ...., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be:$V = -G(2)\left[\frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots\right]$
$= -2G\left[\frac{1}{1 - 1/2}\right] = -4G$
2011 AIPMT-MAINS 1 question
-
A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre will beThe point is at distance $\frac{a}{2}$ from the centre, i.e., inside the shell.
Potential due to the particle at the centre: $V_1 = -\frac{GM}{a/2} = -\frac{2GM}{a}$
Potential inside a spherical shell is constant and equal to its value on the surface: $V_2 = -\frac{GM}{a}$
Total potential: $V = V_1 + V_2 = -\frac{2GM}{a} - \frac{GM}{a} = -\frac{3GM}{a}$
Magnitude of the potential = $\frac{3GM}{a}$
2010 AIPMT-PRE 1 question
-
A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre will beThe point is inside the shell, at a distance $\frac{a}{2}$ from the centre.
Potential due to the particle at the centre: $V_1 = -\frac{GM}{a/2} = -\frac{2GM}{a}$
Potential at any point inside a spherical shell equals that on its surface: $V_2 = -\frac{GM}{a}$
Total potential: $V = V_1 + V_2 = -\frac{2GM}{a} - \frac{GM}{a}$
$V = -\frac{3GM}{a}$