Question

Density of the earth is doubled keeping its radius constant then acceleration, due to gravity will be $-m s^{-2}$ $\left(\mathrm{g}=9.8 \mathrm{~ms}^{2}\right)$ (A) $19.6$ (B) $9.8$ (C) $4.9$ (D) $2.45$

Name: Problem 708, Chapter 6: JEE Physics
Uploaded: 2021-11-14T07:03:08-08:00
Duration: 1 min 42 s
Channel: Narendra Kumar
Description: Density of the earth is doubled keeping its radius constant then acceleration, due to gravity will be -m s^-2 (g=9.8 ms^2) (A) 19.6 (B) 9.8 (C) 4.9 (D) 2.45

   Density of the earth is doubled keeping its radius constant then acceleration, due to gravity will be $-m s^{-2}$
$\left(\mathrm{g}=9.8 \mathrm{~ms}^{2}\right)$
(A) $19.6$
(B) $9.8$
(C) $4.9$
(D) $2.45$

JEE Physics

StemEZ 1st Edition

Chapter 6, Problem 708

Instant Answer

Solved by Expert Narendra Kumar

11/14/2021

Step 1

Step 1: We know that the acceleration due to gravity is given by the formula $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, and $r$ is the radius of the Earth. Show more…

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Density of the earth is doubled keeping its radius constant then acceleration, due to gravity will be $-m s^{-2}$ $\left(\mathrm{g}=9.8 \mathrm{~ms}^{2}\right)$ (A) $19.6$ (B) $9.8$ (C) $4.9$ (D) $2.45$

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Key Concepts

Newton's Law of Universal Gravitation

This law describes the gravitational force between two masses, stating that the force is proportional to the product of the masses and inversely proportional to the square of the distance between them. It is used to calculate the acceleration due to gravity on the surface of a planet using the formula g = GM/R².

Density and Mass Relationship

The mass of an object can be determined from its density and volume, with the relationship mass = density × volume. When the density of an object increases while keeping its volume constant, its mass increases proportionally.

Proportionality of Gravitational Acceleration to Mass

Since the acceleration due to gravity (g) is directly proportional to the mass of the object (when the radius is constant), any change in the mass of the object leads to a proportional change in gravitational acceleration. Doubling the mass, as happens when density is doubled, results in doubling the value of g.

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