Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body ?

Question

Give the location of the centre of mass of a -i- sphere- -ii- cylinder- -iii- ring- and -iv- cube- each of uniform mass density- Does the centre of mass of a body necessarily lie inside the body -

Toppr Admin · Accepted Answer

In all the four cases- as the mass density is uniform- centre of mass is located at their respective geometrical centres-i- Sphere - Centre of Sphereii- Cylinder - Middle Point on axis of cylinderiii- Ring - At centre of ring -Outside the ring-iv- Cube - At point of intersection of diagnolsNo- it is not necessary that the centre of mass of a body should lie on the body- For example- in case of a circular ring- centre of mass is at the centre of the ring- where there is no mass-

Column-I	Column-II
i. Thin uniform hollow cylinder of radius $R$	p. $\frac{2}{5} M R^{2}$
ii. Uniform solid sphere of radius $R$	q. $\frac{2}{3} M R^{2}$
iii. Uniform rectangular lamina of length $l$ and breadth $b$	r. $M R^{2}$
iv. Thin uniform hollow sphere of radius $R$	s. $M (\frac{l^{2} + b^{2}}{12})$