Question

If the diameter of the earth is reduced to half and mass is doubled, then the weight of a body on Earth's surface ________.

Answer 1

Answer:

Explanation:

$Fg_{} = \frac{GMm}{R^{2} }$  

where Fg= gravitational force, G=gravitational constant, M=mass of Earth, m=mass of body, R=radius of Earth

from the above equation, we can say that:

$Fg$ ∝ $\frac{M}{R^{2} }$

Now, after mass of Earth is doubled and diameter is halved (radius is also halved)

$Fg$ ∝ $\frac{2M}{(R/2)^{2} }$

$Fg$ ∝ $\frac{2M}{R^{2}/4 }$

$Fg$ ∝ $\frac{8M}{R^{2} }$

So gravitational force or weight increases by 8 times.

Answer 2

Answer:

diameter is directly proportional to weight and radius square is inversely proportional to weight so weight will be multiplied by 8