JEE Advanced2025PhysicsGravitationActual
Consider a star of mass m₂ ~kg revolving in a circular orbit around another star of mass m₁ ~kg with m₁ m₂ . The heavier star slowly acquires mass from the lighter star at a constant rate of kg / s . In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is r , then its relative rate of change 1 r ~d r ~d t ( . in s .⁻¹ ) is given by: [Note: The original question
Options
- A3 2 m₂
- B2 3 m₂
- C2 m₁
- D3 2 m₁
Correct answer
B. 2 3 m₂
Step-by-step solution
( aligned & v=v₀= G m₁ r & d v₀ d t = v₀ 2 [ m₁ - 1 r d r d t ] aligned ) ( aligned & F =m₂ d v d t & G m₁ r^2 v_r v = d v d t & v₀ r d r d t 1 v₀ = d v d t aligned ) ( V₀ d d t = X₀ 2 [ r m₁ - 1 r d r d t ] ) ( 3 2 1 d d t = r 2 m₁ 1 d r d t = 3 m₂ )