Center of Mass

Distance of centre of mass of a thin uniform semi-circular disc of radius $R$ from its centre is

Mass is distributed uniformly over a thin triangular plate and positions of two vertices are given by $(1, 3)$and $(2, -4)$. What is the position of $3\mathrm{rd}$ vertex if the centre of mass of the plate lies at the centre of origin?

The ball is released from rest. Find centre of mass of large sphere when small sphere reaches the extreme position. 

 List the conditions to increase the stability of a body.

Why is it important to find the centre of mass of a body?

Draw a diagram and explain how to find centre of mass of an irregularly shaped lamina.

The density of a linear rod of length $L$ varies as $\lambda =\frac{{\lambda }_{0}x}{L}$, $x$ is the distance from the left end of rod. Location of centre of mass of the rod, is

Locate centre of mass of a system of three particles, as shown in the figure.

What is centre of gravity of semi-circular disc of radius $\left(R\right)$?

What is the distance of centre of mass from$4 \mathrm{kg}$ mass in the following arrangement:

The particles of mass $1 \mathrm{kg}$, $2 \mathrm{kg}$ and $3 \mathrm{kg}$ are placed at the vertices of an equilateral triangle of side $1 \mathrm{m}$ as shown in the figure. The co-ordinates of centre of mass will be

Four particles having masses $2 \mathrm{kg}$, $3 \mathrm{kg}$, $4 \mathrm{kg}$ and$6 \mathrm{kg}$ are placed at four vertices $A$, $B$, $C$ and $D$ respectively of square of side $1 \mathrm{m}$ as shown in the figure. The position of centre of mass of the system of particles is

A disc of radius$r$is cut from a larger disc of radius$4r$ in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.

In the figure shown a small hole of radius $3 \mathrm{cm}$ is made in a semicircular disc of radius $9 \mathrm{cm}$ а distance $12 \mathrm{cm}$ from the centre C of the disc. The distance (in $\mathrm{cm}$) of centre of mass of this system from point C is :-

 Two rods each of mass $m$ and length$L$ are placed along $X$and $Y$ axis as shown in figure. Coordinates of the centre of mass of the combination is

Linear mass density of rod of length $l$ is directly proportional to $x^3$, where $x$ is distance from one end of rod. Centre of mass of rod lies at a distance

Linear mass density of rod of length $l$ is directly proportional to $x^3$, where $x$ is distance from one end of rod. Centre of mass of rod lies at a distance

In the figure shown a small hole of radius $3 \mathrm{cm}$ is made in a semicircular disc of radius $9\pi \mathrm{cm}$ а distance $12 \mathrm{cm}$ from the centre C of the disc. The distance (in cm) of centre of mass of this system from point C is :-

Find the centre of mass of a thin, uniform disc of radius $R$ from which a small concentric disc of radius $r$ is cut.