- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# How does the weight of an object vary with respect to mass and radius of the earth. In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected?

Formula for the weight of an object: $\boxed{W=mg}$

$W\rightarrow$ Weight

$m\rightarrow$ mass of the object

$g\rightarrow$ acceleration due to gravity

We know that $g=G\frac{M_e}{R^2}$

Here, $G\rightarrow$ gravitational constant

$M_e\rightarrow$ mass of the earth

$R\rightarrow$ radius of the earth

So, weight of the object on earth, $W=m\times G\frac{M_e}{R^2}$

Or $W=G\frac{M_e m}{R^2}$

So, the weight of an object on earth is directly proportional to the masses of the earth and inversely proportional to the square of the radius of the earth.

If the diameter of the earth becomes half, then its radius will also become half$(\frac{R}{2})$ and the mass becomes four times, then the mass of the earth will be $4M_e$.

So, weight of the earth $W\'=G\frac{4M_em}{(\frac{R}{2})^2}$

$=16G\frac{Mem}{R^2}$

$=16W$

Thus the mass of the object will become 16 times if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value.

- Related Questions & Answers
- How do earthquakes affect the geography of the earth?
- Which creature on the earth has the strongest memory?
- What would happen if Earth started to rotate in the opposite direction?
- What is the difference between humans and other species on earth?
- Why is the atmosphere much rarer on the moon than on the earth?
- Medium-Earth Orbit Satellites
- Low-Earth Orbit Satellites
- Who was the first person on Earth according to Hindu mythology?
- C++ program to find the Radius of the incircle of the triangle
- How to set the horizontal and vertical radius of an Ellipse using FabricJS?
- Does JVM creates an object of the Main class?
- Find the center of the circle using endpoints of diameter in C++
- How to set the radius of a Circle using FabricJS?
- How Giving Respect and taking Respect from each others in the Team will Increase the Productivity of whole Organization?
- Calculating the weight of a string in JavaScript
- Who is E Sreedharan and what if he becomes the President of India?