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?

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Solution

The centre of mass (C.M.) is a point where the mass of a body is supposed to be concentrated. For the given geometric shapes having a uniform mass density, the C.M. lies at their respective geometric centres.
The centre of mass of a body need not necessarily lie within it. For example, the C.M. of bodies such as a ring, a hollow sphere, etc., lie outside the body.

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Q. 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 ?

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Q. Column I of the following table gives a list of bodies and column II gives their moments of inertia about the axis of symmetry passing through their centre of mass. Assume mass of each of the bodies is

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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. $\frac{2}{3} M R^{2}$
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iv. Thin uniform hollow sphere of radius $R$	s. $M (\frac{l^{2} + b^{2}}{12})$

Q. Assertion :Centre of mass of a rigid body always lies inside the body. Reason: Centre of mass and centre of gravity coincide if gravity is uniform.

We know centre of mass of a body can lie outside of the body, like in case of a ring. Now let’s take a semicircular ring whose centre is at 0,0. Find the coordinate of it's center of mass.

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Center of Mass

Standard XII Physics

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