Question

Acceleration due to gravity of a body is independent of

• A. mass of the body
• B. altitude of the body
• C. latitude of the body
• D. depth below the earth's surface

Answer 1

The correct option is A

mass of the body

Step 1: Deriving the formula:

Gravitational force is given as,
$F=\frac{GMm}{r^2}$
Now, we know this from Newton's second law of motion,
$F=ma$
$ma=\frac{GMm}{r^2}$
Step 2:

$a=\frac{GM}{r^2}$ $\Rightarrow$$g=\frac{GM}{r^2}$
So, here acceleration due to gravity is represented by (a) which depends on gravitational constant(G), mass of Earth(M) and radius of Earth(R) but it does not depend on mass of body(m). Therefore, the correct answer is (a)