The centroid of a triangle is the intersection of the three medians of the triangle (each median connecting a vertex with the midpoint of the opposite side). For other properties of a triangle’s centroid, see below.

The center of mass can be calculated by taking the masses you are trying to find the center of mass between and multiplying them by their positions. Then, you add these together and divide that by the sum of all the individual masses.

The centre of mass of the solid cone will lie on the altitude at a distance of h/4 distance from the centre of the base of the cone.

The centre of mass of a cone lies on the line joining the apex to the centre of the base at a distance equal to 1/4 of the length of this line from the base.

The center of mass is a position defined relative to an object or system of objects. Sometimes the center of mass doesn’t fall anywhere on the object. The center of mass of a ring for example is located at its center, where there isn’t any material.

Here we will discuss about the area of a circular ring along with some example problems. Therefore, the area of a circular ring = π(R + r) (R – r), where R and r are the radii of the outer circle and the inner circle respectively.

The centre of mass of the ring will lie on the vertical line passing through the centre of the ring. The vertical line is considered as the y-axis. The horizontal line seen in the figure is the x-axis.

of half disc is at distance of 4a3π from centre. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

1 Answer

1. Area of half disc = πR22.
2. Mass per unit area, m = 2MπR2.
3. So, centre of mass of uniform half disc = (0,4R3π)

The centre of mass of the hollow hemisphere will lie on the y-axis, which is the line passing through the centre of the base of the hollow hemisphere. Therefore, the centre of mass of a hollow hemisphere will be at R/2 along the y-axis.

Explanation : Fact that C.O.M. of half disc is at distance of 4a/3π from centre.

Distance of centre of mass of half ring from centre y=π2R=π2×0. 5=π1.

Complete Step-by-Step solution: Let the position of the centre of mass be Xcm on X axis. Let the mass m1 be 2m. Its centre of mass will be on the X-axis which will be equal to L (as can be seen in the figure).

no, It’s not necessary that a mass should be present at the centre of mass of any system. hence, centre of mass is located at (0,0) . here it is clear that each tiny particle doesn’t present in origin but centre of mass of whole system of particles present in origin.

Unlike the scalar product, cross product of two vectors is not commutative in nature.

When finding a cross product you may notice that there are actually two directions that are perpendicular to both of your original vectors. These two directions will be in exact opposite directions. This is because the cross product operation is not communicative, meaning that order does matter.