Q7.20: NCERT Physics - Part 1 GRAVITATION 7.20 Solution: Two stars each of one solar mass ( kg) are approaching each…

Question

Verified Solution • 2025–26 Session moderate

Two stars each of one solar mass (

= 2 \times 10^{30}

kg) are approaching each other for a head on collision. When they are a distance

10^9

km, their speeds are negligible. What is the speed with which they collide? The radius of each star is

10^4

km. Assume the stars to remain undistorted until they collide. (Use the known value of G).

Accepted Answer

**Answer:**

6.4 \times 10^5

m/s **Step-by-Step Explanation:** Using conservation of energy. Initial energy (at distance

d = 10^9

km):

E_i = -\frac{GMM}{d} = -\frac{GM^2}{d}

Final energy (at separation

2R = 2 \times 10^7

m, each moving with speed

v

):

E_f = -\frac{GM^2}{2R} + 2 \times \frac{1}{2}Mv^2

Equating:

Mv^2 = GM^2\left(\frac{1}{2R} - \frac{1}{d}\right)

v = \sqrt{GM\left(\frac{1}{2R} - \frac{1}{d}\right)} = \sqrt{(6.67 \times 10^{-11})(2 \times 10^{30})\left(\frac{1}{2 \times 10^7} - \frac{1}{10^{12}}\right)} = 6.4 \times 10^5 \text{ m/s}

Step-by-Step Verified Solution