Find X centre of mass of four particle system kept at corners of a square of side a?

Question

Answer

Xcm=m(a)+2m(a)/T.m
=am+3am/6m=4am/6m=2a/3

Answer

Finding the Centre of Mass of a Four-Particle System at the Corners of a Square

Introduction

The centre of mass of a system of particles is the point where the system can be considered to be concentrated for the purposes of calculating its motion. In this problem, we need to find the centre of mass of a four-particle system kept at the corners of a square of side a.

Problem Statement

Find the centre of mass of a four-particle system kept at the corners of a square of side a.

Solution

To find the centre of mass of the four-particle system, we can use the following steps:

Draw the square and label the corners as A, B, C, and D.

Assign masses m1, m2, m3, and m4 to particles at corners A, B, C, and D, respectively.

Calculate the position vectors of each particle with respect to an origin at the centre of the square.

Calculate the total mass of the system, M.

Calculate the position vector of the centre of mass, RCM, using the formula RCM = (m1R1 + m2R2 + m3R3 + m4R4) / M, where R1, R2, R3, and R4 are the position vectors of particles 1, 2, 3, and 4, respectively.

Express RCM in terms of the side length, a, of the square.

Conclusion

In conclusion, the centre of mass of a four-particle system kept at the corners of a square of side a can be found by using the above steps. It is important to note that the centre of mass is a point where the system can be considered to be concentrated for the purposes of calculating its motion.

Answer

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