⚛️ Physics · Gravitation · NEET & JEE

Binary stars of mass M each orbit their center of mass at distance d apart. Orbital period T in terms of G, M, d:

Answer: 2*pi*sqrt(d³/(2GM)).

A 2*pi*sqrt(d³/(2GM))
B 2*pi*sqrt(d³/(GM))
C pi*sqrt(d³/(2GM))
D 2*pi*sqrt(d³/(4GM))

Correct answer: A. 2*pi*sqrt(d³/(2GM))

Explanation: Each star orbits at distance d/2 from center. Centripetal force = GM²/d^2. (d/2)x omega² x M = GM²/d^2. omega² = 2GM/d^3. T = 2*pi/omega = 2*pi*sqrt(d³/(2GM)).

g is maximum at Earth's surface; going up, it falls off as 1/r² (inverse-square); going down, it falls off linearly with depth (since only the mass enclosed within radius r contributes), reaching zero at the centre.

Concept context

Universal gravitation, orbital mechanics, gravitational potential, and escape velocity.

Read the full Gravitation notes →

Binary stars of mass M each orbit their center of mass at distance d apart. Orbital period T in terms of G, M, d:

Concept context

More Gravitation questions