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

Answer:

(d) increase by 100%

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

$g_{i} = \frac{Gm_{i}}{R_{i}^{2}}$                             Eq-1

Final acceleration due to gravity of earth is given as

$g_{f} = \frac{Gm_{f}}{R_{f}^{2}}$                             Eq-2

Dividing eq-1 by eq-2

$\frac{g_{i}}{g_{f}} = \frac{m_{i}}{m_{f}}\frac{R_{f}^{2}}{R_{i}^{2}}$

inserting the values

$\frac{g}{g_{f}} = \frac{m_{i}}{(0.5)m_{i}}\frac{(0.5)^{2}R_{i}^{2}}{R_{i}^{2}}$

$g_{f}$ = 2 g

So there is 100% increase