The centre of gravity of a body on the earth coincides with its centre of mass for a small object whereas for an extended object it may not. What is the qualitative meaning of small and extended in this regard ? For which of the following two coincides ? A building, a pond, a lake, a mountain ?
If the vertical height of the object is very small as compared to the earth's radius, it is called object small, else it is extended.
$(1)$ Building and pond are small objects.
$(2)$ A deep lake and a mountain are examples of extended objects.
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 thin metal plate of mass $10 \mathrm{~kg}$ with dimensions is shown. The ratio of $x$ and $y$ coordinates of center of mass of plate in $\frac{n}{9}$. The value of $n$ is $\qquad$
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 centre of mass of the new disc is $\frac{\alpha}{R}$ form the centre of the bigger disc. The value of a is $\alpha $ is
Masses ${\rm{8, 2, 4, 2 }}kg{\rm{ }}$ are placed at the corners $A, B, C, D$ respectively of a square $ABCD$ of diagonal $80\,cm$. The distance of centre of mass from $A$ will be ........ $cm$
A carpenter has constructed a toy as shown in the adjoining figure. If the density of the material of the sphere is $12$ times that of cone, the position of the centre of mass of the toy is given by