Looking for classes? Ksquare Career Institute, Bengaluru →
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 be
A
$\frac{4GM}{a}$
B
$\frac{GM}{a}$
C
$\frac{2GM}{a}$
D
$\frac{3GM}{a}$
Detailed Solution
The 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 = $\frac{3GM}{a}$
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 = $\frac{3GM}{a}$