If f(x) =  x then 

From a uniform circular disc of radius R, a circular disc of radius R/6 and having center at a distance +R/2 from the ceater of the disc is removed. Determine the center of mass of remaining portion of the disc.

Four particles A,B,C and D of masses m,2 m,3 m and 5 m respectively are placed at corners of a square of side x as shown in figure find the coordinate of center of mass take A. at origin of x-y plane

If  and 

Consider a two-particle system with the particles having masses M₁, and m₂. If the first particle is pushed towards the center of mass through a distance d, by what distance should the second particle be moved so as to keep the center of mass at the same position?

For 

There are seven indeterminate forms which are typically considered in the literature
:

Three particles of the same mass lie in the (X,Y) plane, The (X,Y) coordinates of their positions are (1,1),(2,2) and (3,3) respectively. The (X,Y) coordinates of the center of mass are

 given that 

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or 

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or 

If , then the value of  is

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or

Particles of 1gm,1gm,2gm,2gm are placed at the comers A,B,C,D, respectively of a square of side as shown in figure. Find the distance of centre of mass of the system from geometrical center of square.

If  then  has the value

We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means 0 over 0 or 

If  then  is

After the drop detaches its surface energy is