Question

If mass of a planet is eight times the mass of the earth and its radius is twice the radius of the earth, what will be the escape velocity for the planet?
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Answer 1

Answer:

$\huge\mathtt\pink{GIVEN}$

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Planet mass is 8 times that earth

Planet radius is twice then the radius of earth.

Let mass of the Earth = M

Radius of the Earth = R

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Now, we know that The equation to get escape velocity

v = √(2 g r)

v = $\frac{ \sqrt{2GM} }{R}$v=R

2GM

So,If the mass of planet is eight times then escape velocity = 2 √2 times.

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Escape velocity reduced to by 1/√2. If radius expands twice

Hence the net escape velocity will be increase.

2 √2 × (1/√2) = 2 times now.

Now it is clear that the escape velocity of that planet will be 2 times from the earth.

Escape velocity of the earth = 11.2 km/s

Escape velocity of thatplanet.=2 × 11.2

= 22.4 km/sec.

$\large\mathbb\red{AnSwEr}$ = 22.4km per sec

Answer 2

$\bigstar \: \boxed{\sf{\color{Lime}{Steps}}}$

Appropriate Question :-

If the mass of a planet is eight times the mass of the earth and its radius is twice the radius of the earth, what will be the escape velocity of that planet?

Verified Answer :-

Hint: escape velocity of earth 11.2km/sec. The escape velocity depends only on the mass and size of the object from which something is trying to escape. The escape velocity from the Earth is the same for a pebble as it would be for the Space Shuttle.

Complete step by step answer:-

let the mass of earth be Mearth and the mass of planet be Mplanet.

According to the question we know

that Mplanet=8Mearth

Let radius of earth be rearthand radius of the planet be rplanet

According to the question we know that rplanet=2rearth

Equation to calculate the escape velocity of a planet.

vescape=2GM PLANETR

Where G is gravitational

G = Newton's universal constant of gravity

6.67×10−11N/m2/kg3

M= mass of the planet; R = radius of the planet.

So to find the escape velocity for our planet.

vescape=2G8Mearth2Rearth√

vescape=(82√)×2GMearthRearth√

We already know that the escape velocity of earth is 11.2km/sec.

vescape=82√×11.2

∴ vescape=22.4km/sec

The escape velocity of our new planet will be 22.4 km/sec.

Note:-

Other method: We can solve this question by equating the ratio of planet earth and our new planet.

So to find we know,

vescape=2gR√

If mass of the planet is 8 times that of earth

vplanetvearth=MplanetMearth×⇒RearthRplanet√

⇒vplanetveart √

⇒vplanetvearth=2

⇒vplanet=2vearth

⇒vplanet=2×11.2km/sec

∴ vplanet=22.4km/sec

Edit :- If you cant understand, steps I had written as note.

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$\sf\red{Thank\:you!}$