Question

The Escape Velocity from a planet
is v if its mass and radius become
4 and 2 times respectively then
what will be the new escape
veloity?

(1) V
(2) 2V
(3) 1/2V
(4)√2 V​

Answer 1

(4)

$\sqrt{2} v$

Vn for new velocity

Did you understand

Answer 2

The new escape velocity will be (d) √2v.

Given: The escape velocity from a planet is v and the mass and radius become 4 and 2 times respectively.

To Find: The new escape velocity.

Solution:

We know that the escape velocity of a particle from a planet can be given by the formula,

                        V = √( 2 GM / R )                                                   .....(1)

Where V = Escape velocity, G = gravitational constant, M = mass of planet, and R = radius of the planet.

Coming to the numerical, we are given that the escape velocity is v, and mass and radius become 4 and 2 times respectively.

So, new mass M' = 4M

and, new radius R' = 2R

So, we can write the new escape velocity from (1) as,

                        V = √( 2 GM' / R' )

                     ⇒ V = √( 2 G × ( 4M ) / 2R )

                     ⇒ V = √( 2 × 2 GM / R )                                             ....(2)

As we know that escape velocity is v, so we can say that;

                     ⇒ v =√( 2 GM / R )                                                     .....(3)

Substituting (3) in (2), we get;

                     ⇒ V = √2 × v

Hence, the new escape velocity will be (d) √2v.

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