Question

If there is a planet whose mass & radius both are double as that of earth find weight of a body of mass 10 kg on that planet?​

Answer 1

Answer:

of the earth's radius. Determine four times the acceleration due to gravity at the surface of this planet. Acceleration due to gravity at the earth's surface is 10ms

−2

.

Hard

Answer

q

′

=

R

2

GM

=

(4ve)

2

G×2me

=

8

1

ve

2

Gme

=

8

g

To find 4 times the acceleration due to gravity =4×

8

1

g=

2

g

=

2

10

=5m/s

2

Hence, the answer is 5m/s

2

.

Answer 2

⇒G = 6.67 × 10^-11

⇒Mass of the planet = 2Me = 6 × 2 × 10^24 kg

⇒Radius = 2Re = 6.4× 10^6 m

⇒Mass of the object = m = 10 kg.

_______________________________

$ge = \frac{G \: \times M}{ {Re}^{2} } \\ \\ \\ g ′ = \frac{G \: \times 2M }{ {2Re}^{2} } \\ \\ = \frac{2GM}{4Re} \\ \\ = \frac{1}{2} \: \frac{GMm}{Re} \\ \\ = \frac{1}{2} \times 9.8 \\ \\ = 4.9 \: \frac{m}{ {s}^{2} }$

_______________________________

w = mg′

Here w is the weight, m is the mass of the body and g′ is the acceleration due to gravity.

w = 10 × 4.9

w = 49 kg