NEET Physics Practice
Test your knowledge with these challenging questions
Question 20
Two stars each of one solar mass (= 2×10³⁰ kg) are approaching each other for a head on collision. When they are a distance 10⁹ km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 10⁴ km. Assume the stars to remain undistorted until they collide. (Use the known value of G).
Hint: Use conservation of energy. The initial potential energy when the stars are far apart converts to both kinetic and potential energy as they approach each other.
Explanation
Correct Answer: a) 2.58 × 10⁶ m/s
Using conservation of energy:
Initial total energy = -GMM/r
Final total energy = Mv² - GMM/2R
Setting them equal: Mv² - GMM/2R = -GMM/r
Solving for v: v² = GM(1/2R - 1/r)
Substituting values (G = 6.67×10⁻¹¹ Nm²/kg², M = 2×10³⁰ kg, R = 10⁷ m, r = 10¹² m):
v² ≈ 6.67×10⁻¹¹ × 2×10³⁰ × (1/(2×10⁷) = 6.67×10¹²
v ≈ √(6.67×10¹²) ≈ 2.58×10⁶ m/s
The other options are incorrect because:
b) Underestimates by not properly accounting for the potential energy change
c) Overestimates by incorrectly doubling the effect
d) Comes from incorrect unit conversion or calculation error
