An object comprises of $a$ uniform ring of radius $R$ and its uniform chord $AB$ (not necessarily made of the same material) as shown. Which of the following can not be the centre of mass of the object
$(R/3, R/3)$
$(R/3, R/2)$
$(R/ \sqrt 2 , R \sqrt 2)$
both $(B)$ and $(C)$
Write the expression of centre of mass of a system of $'n'$ particles and derive the formula of force acting on its centre of mass.
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
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.......
A spherical cavity of radius $r$ is curved out of a uniform solid sphere of radius $R$ as shown in the figure below. The distance of the centre of mass of the resulting body from that of the solid sphere is given by
A circular plate of uniform thickness has diameter $56\ cm$. A circular part of diameter $42\ cm$ is removed from one edge. What is the position of the centre of mass of the remaining part ........ $cm$.