Which of the following are correct?

Options

A. If `R` is the radius of a planet, `g` is the acceleration due to gravity, the mean density of the planet is `3g//4piGR`
B. Acceleration due to gravity is a universal constant.
C. The escape velocity of a body from earth is `11.2 km s^(-1)`. The escape velocity from a planet which has double the mass of earth and half its radius is `22.4 km s^(-1)`
D. The ratio of gravitational mass and inertial mass of a body at the surface of earth is `1`.

Answer

A, C, D

Explanation

a. `g=(GM)/(R^(2))=G/(R^(2))xx4/3R^(3)rho`
or `rho=(3g)/(2piGR)`
b. Acceleration due to gravity varies from place to place, hence, not correct
c. `v_(e)^(')=sqrt((2G(2M))/(R/2))=2sqrt((2GM)/R)=2xx11.2kms^(-2)=22.4kms^(-1)`
Factual statement.