Three particles of masses 1 ·0 kg, 2 ·0 kg and 3 ·0 kg are placed at the corners A, B and C r

Three particles of masses 1 ·0 kg, 2 ·0 kg and 3 ·0 kg...

Key Concepts

Geometric Analysis of Shapes

Understanding the geometry of the arrangement, such as the properties of a triangle in this context, is crucial. This involves knowing distances, angles, and relationships between vertices, which aids in determining the coordinates of each mass point and, subsequently, the centre of mass.

Coordinate System Setup

Establishing a proper coordinate system is essential for solving problems involving centre of mass in planar geometry. By assigning coordinates to each point where the masses are located, one can use algebraic methods to accurately calculate the centre of mass.

Weighted Average

This concept involves multiplying each component of the position vector by its corresponding mass and then summing these products. Dividing this sum by the total mass of the system yields the weighted average, which is used to compute the centre of mass.

Centre of Mass

The centre of mass is a fundamental concept in mechanics that represents the average position of a system's mass. It is determined by taking the weighted average of the positions of all mass points in the system, thereby providing a single point that effectively summarizes the mass distribution.

Transcript

00:01 In this question, given data is, that is three particle of mass, masses is given, that is first mass is given m1 value is equal to 1 kg, second mass is given m2 that is equal to 2 kg, and the third mass is given that is m3 that is equal to 3 kg.

00:21 Now in the question further, it is saying that these all three masses are placed at corner of equilateral triangle.

00:29 So according to cution, i consider that this is an equilateral triangle and the in the cushion it is saying that first mass m1 is placed at a point and second mass m2 is placed at b point and third mass m3 is placed at c point of this equilateral triangle and further information is the age is given of this triangle that is one meter so i can see that all sides will be written as it is one meter one meter one meter and one meter so this data is given and now in the question it is saying that locate the center of mass so it means we have to find the center of mass of this given system so let's start asking this question so in the answer here i will again drawing this diagram so this is a equilateral triangle and the corners are will be written as it is this is a a b this is a b and this is a c m1 is at a m2 mass will be at b and m3 mass will be at c and i can say that the angle between adjacent sides will be that is 60 degree due to equilateral so all angle will be 60 degree and side value is given that is one meter one meter and one meter now consider that the ab is a x -axis so of ab of this equilateral triangle i will consider that this is the x -axis and so i can say that this is the y -axis so now after making a x -axis and y -axis i can say that the coordinate of a, b and c will be written as it is point a coordinate will be that is zero zero because it is a origin point so i can say that 0 and point b will be written as that is 1 .0 and point c will be written as that is coordinate will be that is half comma is square root of 3 over 2.

02:55 So now i had get the all coordinates of all points so my next step is i will try to find the coordinate of center of mass so consider that the center of mass have a coordinate that is x cm and of y cm so the formula for x cm that means x coordinate of will be written as that is is equal to m1 x1 plus m2 x2 plus m3 x3 plus divided by sorry divided by m1 plus m3 so now next step is put the value of m1, x1, x2, x3, m2, m3, all data.

03:50 So i can say that x cm will be written as that is m1 is 1 kg.

03:57 And here x1, x2, x3 is a coordinate of a, b and c respectively...

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