Question

2. If both the mass and radius of the earth, each decreases by 50%, the acceleration due to gravity would (a) remain same (b) decrease by 50% (c) decrease by 100% (d) increase by 100%

Answer 1

(d) increase by 100%

Step-by-step explanation:

`m_(i)` = initial mass of earth = m

`m_(f)` = final mass of earth = (0.5) m

`R_(i)` = initial radius of earth = R

`R_(f)` = final radius of earth = (0.5) R

`g_(i)` = initial acceleration due to gravity of earth = g

`g_(f)` = final acceleration due to gravity of earth

initial acceleration due to gravity of earth is given as

`g_(i) = (Gm_(i))/(R_(i)^(2))` Eq-1

Final acceleration due to gravity of earth is given as

`g_(f) = (Gm_(f))/(R_(f)^(2))` Eq-2

Dividing eq-1 by eq-2

`(g_(i))/(g_(f)) = (m_(i))/(m_(f))(R_(f)^(2))/(R_(i)^(2))`

inserting the values

`(g)/(g_(f)) = (m_(i))/((0.5)m_(i))((0.5)^(2)R_(i)^(2))/(R_(i)^(2))`

`g_(f)` = 2 g

So there is 100% increase