Q68 / 90 · JEE Main 2024 (30 Jan Shift 2) · Physics

Escape velocity of a body from earth is $11.2 km s^{- 1}$ . If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:

A
$11.2 km s^{- 1}$
B
$8.4 km s^{- 1}$
C
$4.2 km s^{- 1}$
Correct answer
D
$7.9 km s^{- 1}$

Solution

Given: $R_{P} = \frac{R_{E}}{3}, M_{P} = \frac{M_{E}}{6}$
Escape velocity is given by, $v = \sqrt{\frac{2 G M}{R}}$
Therefore,
$v_{E} = \sqrt{\frac{2 G M_{E}}{R_{E}}} . . . (i)$
$v_{P} = \sqrt{\frac{2 G M_{P}}{R_{P}}} . . . (i i)$
$\Rightarrow \frac{v_{E}}{v_{P}} = \sqrt{2}$
$\Rightarrow v_{P} = \frac{v_{E}}{\sqrt{2}} = \frac{11.2}{\sqrt{2}} = 7.9 km s^{- 1}$

Hence, the correct answer is option: 'D'.

Relevant Questions

A body of mass is taken from the surface of earth to a height equal to twice the radius of earth ( ). The increase in potential energy will 05 Apr, 2026 (E)Gravitational potential and Potential Energy
If a body of mass kg falls on the earth from infinity, it attains velocity and kinetic energy on reaching the surface of earth. The values o02 Apr, 2026 (E)Gravitational potential and Potential Energy
Three masses and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigg24 Jan, 2026 (M)Gravitational potential and Potential Energy
The escape velocity from a spherical planet is . The escape velocity from another planet whose density and radius are of those of planet , i22 Jan, 2026 (M)Gravitational potential and Potential Energy
Given below are two statements: one is labelled as Assertion and the other is labelled as Reason Assertion A : The kinetic energy needed to 04 Apr, 2025 (M)Gravitational potential and Potential Energy
An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be 04 Apr, 2025 (E)Gravitational potential and Potential Energy

Escape velocity of a body from earth is 11.2 km s-1. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:

Solution

Relevant Questions

Escape velocity of a body from earth is $11.2 km s^{- 1}$ . If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is: