Some Physics To Do

So if cut down the center of mass, then the left side equals the right side. But the left side is composed of A and the handle and the right side of B. So A+Handle=B which means that A must be less than B.

The further away from the fulcrum of the lever, the larger the moment is, the mass distribution on the left side is not uniform. We intercept the length of both sides to the critical point of change in thickness, and set it as x. Obviously, the part whose length is x on both sides of the fulcrum is the same mass. Now we just have to look at what's beyond x on both sides, the force distance on the left is greater than the torque on the right, the force distance on the left is longer than the right to balance, and the conclusion is that the force distance on the left is greater than the weight on the right, and the weight on the left is less than the weight on the right

[Not a Solution] [Just a comment] You've given us 3 options and we get 3 tries to answer the question. So, Basically anyone can get it right just by hit and trial method.

The moment about the center of mass of both the portion must be equal in order to balance the bat from that portion only. In order to that we must know that "center of mass shifts towards higher mass concentration". Now we see that higher mass concentration is in left portion i.e. B portion. Now moment generated from b is : mass of b multiplied by the distance of center of gravity of b from the center of mass(the place from bat is cut). Now from A portion the moment generated is the addition of two parts i.e. 1)the bat part and 2)the handle part, which is: 1)the bat part multiplied by the distance from center of gravity of bat part from center of mass + 2)mass of handle multiplied by the distance from the middle part of handle plus the length of bat part. Here,we can see for the moments to be equal the product of mass and distance shuould be equal for both portions. One can see that for b Portion the distance is less hence the mass should be more, vice-versa for portion A the distance is more hence the mass should be less.