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

If  the......... radius of the drop when it detaches from the dropper is approximately

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

If the radius of the opening of the dropper is $r$, the vertical force due to the surface tension on the drop of radius $R$ (assuming $r<<R$) is: