Question:
The escape velocity of a body from the earth is $v_{e}$ . If the radius of earth contracts to $ \frac{1}{4}th $ of its value, keeping the mass of the earth constant, the escape velocity will be
The escape velocity of a body from the earth is $v_{e}$ . If the radius of earth contracts to $ \frac{1}{4}th $ of its value, keeping the mass of the earth constant, the escape velocity will be
Updated On: Jun 6, 2024
- doubled
- halved
- tripled
- unaltered
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Escape velocity $v_{e}=\sqrt{\frac{2 G M}{R}}$
If $R'=\frac{R}{4}$
$v_{e}'=2 \sqrt{\frac{2 G M}{R}}$
Since, $G$ and $M$ are constant,
hence $v_{e}'=2 v_{e}$
Was this answer helpful?
0
0
Top Questions on Gravitation
- An object of mass 100 kg falls from point A to B as shown in figure. The change in its weight, corrected to the nearest integer is ($R_E$ is the radius of the earth):
- NEET (UG) - 2024
- Physics
- Gravitation
- The escape velocity for earth is v. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:
- NEET (UG) - 2024
- Physics
- Gravitation
- A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is:
- JEE Main - 2024
- Physics
- Gravitation
- A light planet is revolving around a massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the force of attraction between the planet and the star is proportional to $R^{-\frac{3}{2}}$, then choose the correct option:
- JEE Main - 2024
- Physics
- Gravitation
- Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?
- JEE Main - 2024
- Physics
- Gravitation
View More Questions
Questions Asked in JKCET exam
- A moving block having mass $m$, collides with another stationary block having mass $4\,m$. The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v$, then the value of coefficient of restitution (e) will be
- JKCET - 2019
- work, energy and power
- A force $ F = 3x^2 + 2x + 1 $ acts on a body in the $ x $ -direction. The work done by this force during a displacement from $ x = -1 $ to $ +1 $ is
- JKCET - 2019
- work, energy and power
- What is the colour of the flame on heating potassium in the flame of a Bunsen burner?
- JKCET - 2019
- GROUP 1 ELEMENTS
- If $ a $ , $ b $ , $ c $ are the lengths of three edges of unit cell, $ \alpha $ is the angle between side $ b $ and $ c $ , $ \beta $ is the angle between side $ a $ and $ c $ and $ \gamma $ is the angle between side $ a $ and $ b $ , what is the Bravais Lattice dimensions of a tetragonal crystal?
- JKCET - 2019
- The solid state
- Which of the following compounds is known as copper glance?
- JKCET - 2019
- General Principles and Processes of Isolation of Elements
View More Questions
Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].