
A body weighs $500N$ on the surface of the earth. How much would it weigh half-way below the surface of the earth?
(A) $125N$
(B) $250N$
(C) $500N$
(D) $1000N$
Answer
164.1k+ views
Hint: In order to solve this question, we should know that mass of the body doesn’t change with the height from the surface of the earth but the acceleration due to gravity changes and thus change in weight appears, here half below the surface of the earth is half of the radius of the earth.
Formula used:
If g is the acceleration due to gravity on the surface of the earth, R is the radius of the earth and h is the height below the surface of the earth then, acceleration due to gravity at this height g’ is given by $g' = g(1 - \dfrac{h}{R})$
The weight of a body of mass m is given by $W = mg$
Complete answer:
We have given that weight of a body at the surface of the earth is $W = 500N$
Now, acceleration due to gravity at half distance from the surface of the earth which means $h = \dfrac{R}{2}$ is given by the formula $g' = g(1 - \dfrac{h}{R})$on putting the value we get,
$
g' = g(1 - \dfrac{R}{{2R}}) \\
g' = \dfrac{g}{2} \to (i) \\
$
On multiplying the equation (i) by the mass of the body m we get,
$mg' = m\dfrac{g}{2} \to (ii)$ now, since weight of a body is given by $W = mg$
So at the height of $h = \dfrac{R}{2}$ below the surface of the earth the weight of the body will by $W' = mg'$ and original weight a the surface of the earth is given to us $W = mg = 500N$, On putting these values in equation (ii) we get,
$
W' = \dfrac{W}{2} \\
W' = \dfrac{{500}}{2} \\
W' = 250N \\
$
So, the weight of the body at half below the surface of the earth is $250N$
Hence, the correct option is (B) $250N$
Note:It should be remembered that mass is the inherent property of matter whereas weight is the actual force acting on the body due to acceleration due to gravity and weight changes with places whereas mass remains constant as long as there is no relativistic effect on the body.
Formula used:
If g is the acceleration due to gravity on the surface of the earth, R is the radius of the earth and h is the height below the surface of the earth then, acceleration due to gravity at this height g’ is given by $g' = g(1 - \dfrac{h}{R})$
The weight of a body of mass m is given by $W = mg$
Complete answer:
We have given that weight of a body at the surface of the earth is $W = 500N$
Now, acceleration due to gravity at half distance from the surface of the earth which means $h = \dfrac{R}{2}$ is given by the formula $g' = g(1 - \dfrac{h}{R})$on putting the value we get,
$
g' = g(1 - \dfrac{R}{{2R}}) \\
g' = \dfrac{g}{2} \to (i) \\
$
On multiplying the equation (i) by the mass of the body m we get,
$mg' = m\dfrac{g}{2} \to (ii)$ now, since weight of a body is given by $W = mg$
So at the height of $h = \dfrac{R}{2}$ below the surface of the earth the weight of the body will by $W' = mg'$ and original weight a the surface of the earth is given to us $W = mg = 500N$, On putting these values in equation (ii) we get,
$
W' = \dfrac{W}{2} \\
W' = \dfrac{{500}}{2} \\
W' = 250N \\
$
So, the weight of the body at half below the surface of the earth is $250N$
Hence, the correct option is (B) $250N$
Note:It should be remembered that mass is the inherent property of matter whereas weight is the actual force acting on the body due to acceleration due to gravity and weight changes with places whereas mass remains constant as long as there is no relativistic effect on the body.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
