NEET Exam  >  NEET Questions  >  Four particles each of mass m placed at corne... Start Learning for Free
Four particles each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain?
Most Upvoted Answer
Four particles each of mass m placed at corners of square of side leng...
Community Answer
Four particles each of mass m placed at corners of square of side leng...
Problem Statement:
Four particles, each of mass m, are placed at the corners of a square of side length l. The radius of gyration of the system about an axis perpendicular to the square and passing through the center is to be determined.

Solution:
To find the radius of gyration of the system, we need to calculate the moment of inertia and the total mass of the system.

Step 1: Calculate the Moment of Inertia:
The moment of inertia of a point mass rotating about an axis passing through its center of mass is given by the equation I = m*r^2, where I is the moment of inertia, m is the mass, and r is the distance of the mass from the axis of rotation.

In this case, all four particles are at the corners of the square, and the axis of rotation passes through the center of the square. Therefore, the distance of each particle from the axis of rotation is l/2.

The moment of inertia of each particle is m*(l/2)^2 = ml^2/4.

Since there are four particles, the total moment of inertia of the system is 4*(ml^2/4) = ml^2.

Step 2: Calculate the Total Mass:
Since each particle has mass m, the total mass of the system is 4m.

Step 3: Calculate the Radius of Gyration:
The radius of gyration of the system is given by the equation k = sqrt(I/m), where k is the radius of gyration, I is the moment of inertia, and m is the total mass.

Substituting the values of moment of inertia (ml^2) and total mass (4m) into the equation, we get k = sqrt(ml^2/4m) = sqrt(l^2/4) = l/2.

Therefore, the radius of gyration of the system is l/2.

Step 4: Verify the Answer:
To verify that the given answer is correct, we can calculate the moment of inertia of the system using the parallel axis theorem.

The moment of inertia of a system of particles can be calculated by summing the individual moments of inertia of each particle and adding the term m*d^2, where m is the mass of the particle and d is the distance between the particle and the axis of rotation.

For the given system, the distance between each particle and the axis of rotation is l/2. Therefore, the moment of inertia of the system can be calculated as follows:

I = 4*(ml^2/4) + 4*(m*(l/2)^2) = ml^2 + ml^2 = 2ml^2.

Now, we can calculate the radius of gyration using the formula k = sqrt(I/m):

k = sqrt(2ml^2/4m) = sqrt(l^2/2) = l/sqrt(2).

Hence, the calculated radius of gyration matches the given answer of l/sqrt(2).
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 each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain?
Question Description
Four particles each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain? 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 each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four particles each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain?.
Solutions for Four particles each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain? 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 each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain? defined & explained in the simplest way possible. Besides giving the explanation of Four particles each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain?, a detailed solution for Four particles each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain? has been provided alongside types of Four particles each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain? theory, EduRev gives you an ample number of questions to practice Four particles each of mass m placed at corners of square of side length l . tha radius of gyration vof system about an axis perpendicular to square and passing through centre is ? answer is l/ sq root 2 pls explain? 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