Xcm =5(0)+10×1/10+5
=10/15
= 2/3
=0.67m
=67 cm

Introduction:

The problem involves two particles of masses 5kg and 10kg respectively, attached to the two ends of a rigid rod with negligible mass. We need to determine the distance of the center of mass of the system from the 5kg particle.

Center of Mass:

The center of mass of a system is the point where the total mass of the system can be assumed to be concentrated. It is the average position of all the particles in the system, weighted by their respective masses.

Calculation of Center of Mass:

To calculate the center of mass of this system, we need to consider the masses and positions of both particles. Let's assume that the 5kg particle is located at point A and the 10kg particle is located at point B.

Step 1: Finding the position of the center of mass of the 5kg particle:

Since the 5kg particle is located at one end of the rod, its position is defined as x1 = 0m. The mass of the 5kg particle is m1 = 5kg. Therefore, the contribution of the 5kg particle to the center of mass is:

m1*x1 = 5kg * 0m = 0kgm

Step 2: Finding the position of the center of mass of the 10kg particle:

Since the 10kg particle is located at the other end of the rod, its position is defined as x2 = 1m. The mass of the 10kg particle is m2 = 10kg. Therefore, the contribution of the 10kg particle to the center of mass is:

m2*x2 = 10kg * 1m = 10kgm

Step 3: Finding the total mass of the system:

The total mass of the system is the sum of the masses of both particles:

M = m1 + m2 = 5kg + 10kg = 15kg

Step 4: Finding the position of the center of mass of the system:

The position of the center of mass of the system, xcm, can be calculated using the formula:

xcm = (m1*x1 + m2*x2) / M

Substituting the values we calculated earlier:

xcm = (0kgm + 10kgm) / 15kg = 10/15 = 2/3 m

Conclusion:

The center of mass of the system is located at a distance of 2/3 m from the 5kg particle.