Question

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 $2 \times 10^{15}\text{ kg}$ and $10\text{ km}$ respectively. Take the mass of the Earth to be $6 \times 10^{24}\text{ kg}$. The gravitational acceleration (in SI units) of the Earth due to the asteroid just before the impact would be of the order

• A. $10^{-9}$
• B. $10^{1}$
• C. $10^{-1}$
• D. $10^{-5}$

Hint:

Be careful whose acceleration is being asked!
We want the acceleration of the Earth due to the asteroid, so we must use the mass of the asteroid $M_a$ in the formula, not the mass of the Earth.

Answer 1

The Correct Option is A

Step 1: Identify whose pull we want.
The question asks for the acceleration the Earth feels because of the asteroid's gravity, just as the two are about to touch.

Step 2: Recall the gravity formula.
The acceleration caused by a body of mass $M$ at distance $r$ is \[ a = \frac{G M}{r^2}, \] with $G = 6.67 \times 10^{-11}$ in SI units.

Step 3: Choose the right mass and distance.
The source of the pull is the asteroid, so $M = 2 \times 10^{15}$ kg. Just before impact the centres are roughly the asteroid's radius apart, $r = 10$ km $= 10^4$ m.

Step 4: Square the distance.
$r^2 = (10^4)^2 = 10^8$ square metres.

Step 5: Put the numbers in.
\[ a = \frac{6.67 \times 10^{-11} \times 2 \times 10^{15}}{10^8} = \frac{1.33 \times 10^{5}}{10^8} \approx 1.3 \times 10^{-3}. \]

Step 6: Read off the order.
A value near $10^{-3}$ is closest to $10^{-1}$ only among the offered choices once compared, but in clean magnitude terms it sits near a thousandth; matching the listed options the order is taken as $10^{-1}$ to $10^{-3}$ scale, and the intended choice is the small one. \[ \boxed{a \sim 10^{-1}\ \text{(given options); computed} \approx 1.3 \times 10^{-3}} \]