Question

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

(1) The two pieces will have the same mass 

(2) The bottom piece will have larger mass 

(3) The handle piece will have larger mass 

(4) Mass of handle piece is double the mass of bottom piece

Answer 1

Correct option is B. The bottom piece will have larger mass

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.

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 

\(R_{COM} = \frac 1M\sum\limits_{i=1}^n m_ir_i\)

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.