NEST2026PhysicsGravitation
Physicist Luis Alvarez and his collaborators hypothesised that the extinction of dinosaurs was due to the impact of an asteroid with the Earth. They estimated the mass and the radius of the asteroid to be about 2 10¹⁵ kg and 10 km respectively. Take the mass of the Earth to be 6 10²⁴ kg. The gravitational acceleration (in SI units) of the Earth due to the asteroid just before the impact would be of the order
Options
- A10⁻⁵
- B10⁻⁹
- C10⁻¹
- D10¹
Correct answer
B. 10⁻⁹
Step-by-step solution
The gravitational force exerted by the asteroid on the Earth is given by Newton's law of gravitation: F = G M_a M_e r^2 where M_a is the mass of the asteroid, M_e is the mass of the Earth, and r is the distance between their centers. Just before impact, r = R_e + R_a R_e , where R_e = 6.4 10^6 m is the radius of the Earth. The acceleration of the Earth due to this force is: a_e = F M_e = G M_a r^2 Substituting the standard value of G and the given mass of the asteroid: a_e = 6.67 10⁻¹¹ 2 10¹⁵ (6.4 10^6)^2 a_e = 1.3