Question

The ratio of escape velocity at earth (V_e) to the escape velocity at a planet (v_p) whose radius and mean density are twice as that of earth is,

1: $2 square root of 2$

1:4

1: $square root of 2$

1:2

Solution

1: $2 square root of 2$

Escape velocity of earth can be given as,
v_e = $square root of 2 gR end root$ = R $square root of 8 over 3 πGρ end root$ , where $straight rho$ is the density of the earth.
$rightwards double arrow space straight v subscript straight e space equals space straight R square root of 8 over 3 πGρ end root$ ... (i)
Given that the radius and mean density of planet are twice as that of earth.
So, escape velocity at planet will be,
$straight v subscript straight p space equals space 2 straight R space square root of 8 over 3 πG 2 straight rho end root space space space... space left parenthesis ii right parenthesis Dividing space eqn. space by space left parenthesis straight i right parenthesis space by space left parenthesis ii right parenthesis comma straight v subscript straight e over straight v subscript straight p space equals space fraction numerator straight R square root of 8 over 3 πGρ end root space over denominator 2 straight R square root of 8 over 3 πG 2 straight rho end root end fraction rightwards double arrow space straight v subscript straight e over straight v subscript straight p space equals fraction numerator 1 over denominator 2 square root of 2 end fraction$

Some More Questions From Wave Optics Chapter

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

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Wave Optics

The ratio of escape velocity at earth (V_e) to the escape velocity at a planet (v_p) whose radius and mean density are twice as that of earth is,

1: $2 square root of 2$

1:4

1: $square root of 2$

1:2

Some More Questions From Wave Optics Chapter

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

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For Daily Free Study Material Join wiredfaculty

Wave Optics

The ratio of escape velocity at earth (Ve) to the escape velocity at a planet (vp) whose radius and mean density are twice as that of earth is, 1: 1:4 1: 1:2

Some More Questions From Wave Optics Chapter

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The ratio of escape velocity at earth (V_e) to the escape velocity at a planet (v_p) whose radius and mean density are twice as that of earth is,

1: $2 square root of 2$

1:4

1: $square root of 2$

1:2