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aalyn [17]
3 years ago
7

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

crease by 50% (c) decrease by 100% (d) increase by 100%
Geography
1 answer:
Scrat [10]3 years ago
8 0

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

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