Question

The mass and radius of a planet are eight times and two times the mass and radius of the Earth, respectively. Then, the acceleration due to gravity of the planet is _________ times the acceleration due to gravity on the Earth. (Take g = 10 m s^-2)

• A. eight
• B. four
• C. two
• D. three

Answer 1

The correct option is C

two

Step 1, Given data

The mass of the planet is eight times the mass of the earth.

The radius of the planet is two times the radius of the earth.

Step 2, Finding the Acceleration due to gravity

We know,

$g=\frac{GM}{R^2}$

Where, g = Acceleration due to gravity, G = Universal constant, M = Mass of the planet, R = radius of the planet

Now, We can write,

$Accelerationduetogravityattheplanet=\frac{G\times 8\times M}{{\left({\displaystyle 2R}\right)}^2}=2\frac{GM}{R^2}$

So, Acceleration due to gravity on the planet is 2 times the acceleration due to gravity on the earth

Hence the correct option is (C)