Composite & Cut-Out Bodies

Figure shows a composite system of two uniform rods of length as shown. The co-ordinates of the centre of mass of the system of rods are

Three rods of same mass are placed as shown in figure. The co-ordinates of centre of mass of the system are

A rod of length 5 L is bent right angle keeping one side length as 2 L.

The position of the centre of mass of the system:

(Consider $L = 10\text{ cm}$)

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

A uniform thin metal plate of mass $10\text{ kg}$ with dimensions is shown. The ratio of $x$ and y coordinates of center of mass of plate is $\frac{n}{9}$. The value of $n$ is ________.

A circular hole of radius $\left(\frac{a}{2}\right)$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be:

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are:

As shown in figure, when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centered at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, on the surface of the cavity. R can be determined by the equation:

A square shaped hole of side l = $\frac{a}{2}$ is carved out at a distance d = $\frac{a}{2}$ from the centre ‘O’ of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is $-\frac{a}{X}$, value of X (to the nearest integer) is:

The position vector of the centre of mass$\vec{r}_{cm}$ of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :-

In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then $\frac{BC}{AB}$ is close to:

A circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs coincide. The center of mass of the new disc is $\alpha R$ from the center of the bigger disc. The value of $\alpha$ is

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $'\vec{F}'$ is applied at the point $P$ parallel to $AB,$ such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C.$