Question

if mass of planet is eight eight time mass of earth and its radius is twice of the radius of the earth what will be the escape velocity for that planet

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Answer 1

Given :

• Mass of a planet is eight times the mass of earth
• Radius of a planet is twice the radius of earth

To Find :

• Escape velocity for that planet

Solution :

Escape velocity for a planet is given by ,

$\\ \star \: {\boxed{\purple{\sf{v = \sqrt{ \dfrac{2GM }{R} } }}}}$

Where ,

• M is mass of planet
• R is radius of planet

Let the mass of earth be M and radius be R. Then the mass of a planet becomes 8M and radius becomes 2R [given condition].

Now , Calculating escape velocity for earth ;

$\\ : \implies \sf \:v_{(earth)} = \sqrt{ \dfrac{2GM }{ R} } \: .........(1)$

Now , Calculating escape velocity of the planet ;

$\\ : \implies \sf \: v_{(planet)} = \sqrt{\dfrac{2(8M)}{(2 R)} }$

$\\ : \implies \sf \: v_{(planet)} = \sqrt{ \dfrac{2(4M )}{R} }$

$\\ : \implies \sf \: v_{(planet)} = 2 \sqrt{ \dfrac{2GM }{R} }$

$\\ : \implies \sf \: v_{(planet)} = 2[ v_{(earth)} ]$

Escape velocity of earth is 11.2 km/s. Now,

$\\ : \implies \sf \: v_{(planet)} = 2 \times 11.2 \: km. {s}^{ - 1}$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{v_{(planet)} = 22.4 \: km .{s}^{ - 1} }}}}} \: \bigstar$

Hence ,

• The escape velocity of a planet whose mass of planet is eight eight time mass of earth and radius is twice of the radius of the earth is 22.4 km/s.

Answer 2

꧁༺TheBrainlyopekaa༻꧂

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✧Given in the question :-

߷︎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

➣Now, we know that The equation to get escape

velocity.

☛v = √(2 g r)

☛v=2GM_R

➣ If the mass of planet is eight times then

escape velocity = 2 √2 times.

➣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 that planet = 2 × 11.2 = 22.4

➥km/sec.

➥Hence the escape velocity of that planet will

➥be 22.4 km/s

➥Hope it Helps :-)

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꧁༺TheBrainlyopekaa༻꧂