(C) The escape velocity $(v_e)$ of an object from the surface of a planet is given by the formula:$v_e = \sqrt{\frac{2GM}{R}}$Where:$G$ is the univers

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(C) The escape velocity $(v_e)$ of an object from the surface of a planet is given by the formula:$v_e = \sqrt{\frac{2GM}{R}}$Where:$G$ is the universal gravitational constant,$M$ is the mass of the planet,$R$ is the radius of the planet.From the formula,it is clear that the escape velocity depends only on the mass $(M)$ and the radius $(R)$ of the planet.It does not depend on the mass of the escaping particle or the temperature of the planet.Therefore,the correct factors are $I$ and $IV$.

Class 11 Physics Gravitation Escape Velocity and Escape Energy

Medium

Gas escapes from the surface of a planet because it acquires an escape velocity. The escape velocity will depend on which of the following factors :
$I.$ Mass of the planet
$II.$ Mass of the particle escaping
$III.$ Temperature of the planet
$IV.$ Radius of the planet
Select the correct answer from the codes given below :

A
$I$ and $II$
B
$II$ and $IV$
C
$I$ and $IV$
D
$I, III$ and $IV$

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Class 11

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Gravitation

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Escape Velocity and Escape Energy

$A$ rocket is fired vertically with a speed of $4 \ km/s$ from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth (in $km$)? (Take radius of Earth $R = 6.4 \times 10^6 \ m$ and $g = 10 \ m/s^2$)

MediumTS EAMCET 2022

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$A$ body is projected up with a velocity equal to $\frac{3}{4}$ of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth $= R$)

EasyTS EAMCET 2002

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Does the escape speed of a body from the Earth depend on:
$(a)$ the mass of the body,
$(b)$ the location from where it is projected,
$(c)$ the direction of projection,
$(d)$ the height of the location from where the body is launched?

Medium

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$A$ body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth,the maximum height attained by the body from the surface of the earth is

DifficultTS EAMCET 2009

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The escape velocity of an object from the Earth depends upon the mass of the Earth $(M)$,its mean density $(\rho)$,its radius $(R)$,and the gravitational constant $(G)$. Thus,the formula for escape velocity is:

Medium

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$A$ rocket is fired vertically with a speed of $4 \ km/s$ from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth (in $km$)? (Take radius of Earth $R = 6.4 \times 10^6 \ m$ and $g = 10 \ m/s^2$)

$A$ body is projected up with a velocity equal to $\frac{3}{4}$ of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth $= R$)

Does the escape speed of a body from the Earth depend on:$(a)$ the mass of the body,$(b)$ the location from where it is projected,$(c)$ the direction of projection,$(d)$ the height of the location from where the body is launched?

$A$ body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If $R$ is the radius of the earth,the maximum height attained by the body from the surface of the earth is

The escape velocity of an object from the Earth depends upon the mass of the Earth $(M)$,its mean density $(\rho)$,its radius $(R)$,and the gravitational constant $(G)$. Thus,the formula for escape velocity is:

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Does the escape speed of a body from the Earth depend on:
$(a)$ the mass of the body,
$(b)$ the location from where it is projected,
$(c)$ the direction of projection,
$(d)$ the height of the location from where the body is launched?