NEET Exam  >  NEET Questions  >  Four particles of mass m,2m,3m,4m kept in a s... Start Learning for Free
Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be?
Most Upvoted Answer
Four particles of mass m,2m,3m,4m kept in a sequence at the corner of ...
Gravitational Force on a Particle at the Center of a Square

To find the magnitude of the gravitational force acting on a particle of mass m placed at the center of a square, we need to consider the gravitational forces exerted by each of the four particles in the sequence.

Gravitational Force Calculation

The gravitational force between two objects is given by Newton's Law of Universal Gravitation:

F = G * (m1 * m2) / r^2

Where:
- F is the gravitational force between the two objects
- G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects

Gravitational Forces from Each Particle

Let's consider each particle in the sequence and calculate the gravitational force exerted by it on the particle at the center of the square.

1. Particle of mass m:
The distance between the particle at the center and the particle of mass m is the length of the side of the square, which is "a". Therefore, the gravitational force exerted by this particle is:
F1 = G * (m * m) / a^2

2. Particle of mass 2m:
The distance between the particle at the center and the particle of mass 2m is the diagonal of the square, which can be calculated using the Pythagorean theorem. The length of the diagonal is √2a. Therefore, the gravitational force exerted by this particle is:
F2 = G * (m * 2m) / (√2a)^2 = G * (2m^2) / 2a^2 = G * m^2 / a^2

3. Particle of mass 3m:
The distance between the particle at the center and the particle of mass 3m is also the diagonal of the square, which is √2a. Therefore, the gravitational force exerted by this particle is:
F3 = G * (m * 3m) / (√2a)^2 = G * (3m^2) / 2a^2

4. Particle of mass 4m:
The distance between the particle at the center and the particle of mass 4m is the diagonal of the square, which is √2a. Therefore, the gravitational force exerted by this particle is:
F4 = G * (m * 4m) / (√2a)^2 = G * (4m^2) / 2a^2 = 2G * m^2 / a^2

Net Gravitational Force

To find the net gravitational force on the particle at the center, we need to sum up the forces from each particle:

Net Force = F1 + F2 + F3 + F4
= G * (m^2 / a^2) + G * (m^2 / a^2) + G * (3m^2 / 2a^2) + 2G * (m^2 / a^2)
= (5G * m^2 / a^2) + (3G * m^2 / 2a
Community Answer
Four particles of mass m,2m,3m,4m kept in a sequence at the corner of ...
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
Explore Courses for NEET exam

Top Courses for NEET

Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be?
Question Description
Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be?.
Solutions for Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be? in English & in Hindi are available as part of our courses for NEET. Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be? defined & explained in the simplest way possible. Besides giving the explanation of Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be?, a detailed solution for Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be? has been provided alongside types of Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be? theory, EduRev gives you an ample number of questions to practice Four particles of mass m,2m,3m,4m kept in a sequence at the corner of a square of side "a" magnitude of gravitational force acting on a particle of mass m , placed at the centre of the square will be? tests, examples and also practice NEET tests.
Explore Courses for NEET exam

Top Courses for NEET

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev