Question

Escape velocity of body on the surface of the earth is 11.2 km per second if the earth mass increases to twice its present value and the radius of the earth become half the escape velocity would become

Answer 1

ESCAPE VELOCITY IS GIVEN BY :-

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Vesc= SQUARE ROOT 2 GM÷R

ESCAPE VELOCITY OF EARTH IS 11.2km/sec

GIVEN DATA :-

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MASS IS INCREAED TO TWICE =M' = 2M

RADIUS IS HALVED = R' =R÷2

Vesc = SQUARE ROOT 2 G 2M÷ R÷2 (2 OF R÷2 WILL BE MOVE UPWARD AND WILL MULTIPLY WITH 2 OF MASS )

Vesc' = SQUARE ROOT 2 G 4M÷R (square root 4 is equal to 2 so it will come out of square root )

Vesc' = 2 (SQUARE ROOT 2 G M÷R )

WE KNOW THAT SQUARE ROOT 2GM÷R IS EQUAL TO vesc

SO

Vesc' = 2 Vesc

Vesc' = 11.2 × 2 =22.4 km/sec

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