Question

A cricket bat is cut at the location of its centre of mass as shown. Then: -

A. The two pieces will have the same mass
B. The bottom piece will have larger mass
C. The handle piece will have larger mass
D. Mass of handle piece is double the mass of bottom piece

Answer 1

Centre of mass of a distributed mass system is an imaginary point where whole mass of the system seems to be concentrated. Centre of mass is a unique point for a system. Centre of mass lies near to the heavier part of the body.

Complete step by step answer:
Centre of mass lies near to the heavier part of the body. As the bottom part of the cricket bat lies closer to the centre of mass as compared with the handle piece of the bat, it can be concluded that the bottom part of the bat is heavier. In other words, the bottom piece will have larger mass.
Hence, option B is correct.
Additional information: Centre of mass of a system is defined as an imaginary point where the whole mass of the system seems to be concentrated. It is the balance point of the system. At this point, weighted position vectors of all the masses of a system adds to zero.
Centre of mass lies near to the heavier part of the body. Mathematically, centre of mass for a system of particles is written as
${{R}_{COM}}=\dfrac{1}{M}\sum\limits_{i=1}^{n}{{{m}_{i}}{{r}_{i}}}$
Where ${{m}_{i}}$ and ${{r}_{i}}$ are the mass and co-ordinates of particle $i$ respectively. $M$ is the total mass of the whole system.

Note:
For regular shaped objects with uniform mass density, the centre of mass lies at centroid. This statement may not be true for objects with non-uniform density. For objects whose dimensions are much smaller than the radius of earth, centre of mass and centre of gravity coincide. Centre of mass lies near the heavier portion of a system.