Solve Study Textbooks Guides

Use app

Login

>>Class 11
>>Physics
>>Gravitation
>>Variation in Value of Acceleration due to Gravity
>> $The density of newly discovered planet i$

Question

The density of newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be:

A

$\frac{1}{2} R$

B

2R

C

4R

D

$\frac{1}{4} R$

Hard

Open in App

Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is A)

Given that, $ρ_{p l a n e t = 2 ρ_{e a r t h}}$
$g_{p l a n e t = 2 g_{e a r t h}}$
$g = \frac{G M}{R ^{2}} \times \frac{\frac{4}{3} π R ^{3}}{\frac{4}{3} π R ^{3}} g = \frac{4}{3} π ρ G R ∴ \frac{g _{p l a n e t}}{g _{e a r t h}} = \frac{ρ _{p} R _{p}}{ρ _{e} R _{e}} ∴ R_{p} = \frac{ρ _{e} R}{ρ _{p}} \Rightarrow \frac{ρ _{e} R}{2 ρ _{p}} R_{p} = \frac{R}{2}$

Solve any question of Gravitation with:-

Patterns of problems

Was this answer helpful?

0

0

Similar questions

The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is $9 : 4$ . The mass of the planet is $\frac{1}{9} t h$ of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ?
(Take the planets to have the same mass density)

The mass of a planet is twice the mass of earth and diameter of the planet is thrice the diameter of the earth, then the acceleration due to gravity on the planet's surface is:

The acceleration due to gravity on the surface of a planet whose mass is same as that of the Earth and radius is half of that of the Earth is:
(Mass of Earth: $6 \times 1 0^{24} k g$ and Radius of Earth: $6.4 \times 1 0^{3} k m$ )

If g is acceleration due to gravity at the surface of the earth of radius R, the mass of the earth is :

If the density of a small planet is the same as that of earth, while the radius of the planet is $0.2$ times that the earth, the gravitational acceleration on the surface of that planet is:

More From Chapter

View chapter >

Revise with Concepts

Variation in the Value of Acceleration Due to Gravity

ExampleDefinitionsFormulaes

Learn with Videos

Variation in acceleration due to gravity

Acceleration due to gravity and its variation with height

Shortcuts & Tips

Important Diagrams

Common Misconceptions

Problem solving tips

Memorization tricks

Practice more questions

JEE Mains Questions

AIIMS Questions

Medium Questions