Which of the following is a false statement? select one:
a. for an object on the surface of the earth, the center of gravity and the center of mass are the same point.
b. for a uniform symmetric object, the center of mass is at the center of symmetry.
c. the center of gravity of an object may be thought of as the "balance point."
d. the center of mass of an object must lie within the object.

The false statement is in option 'd': The center of mass of an object must lie within the object.

Explanation:

Center of mass is a theoretical point in a system of particles where the whole mass of the system is assumed to be concentrated.

Mathematically the position vector of center of mass is defined as

where,

is the position vector of the mass dm.

As we can see for homogenous symmetrical objects such as a sphere,cube,disc the center of mass is located at the centroid of the shapes itself but in many shapes it is located outside the body also.

Examples of shapes in which center of mass is located outside the body:

1) Horseshoe shaped body.

2) A thin ring.

In many cases we can make shapes of bodies whose center of mass lies outside the body.

d.7.5cm is your answer