The system in the figure consists of 5 point particles. Four identical point par

Question

The system in the figure consists of 5 point particles. Four identical point particles, each with mass m, are positioned at the corners of a square with sides d.The fifth point particle has a mass 2m and is located a distance 2d from the center of the square formed by the other four point particles, along a direction perpendicular to the square.

What is the distance (in cm) from the point particle with mass 2m to the center of mass of this system if d = 12 cm and m = 0.01 kg?

The system in the figure consists of 5 point particles. Four identical point particles, each with mass m, are positioned at the corners of a square with sides d.The fifth point particle has a mass 2m and is located a distance 2d from the center of the square formed by the other four point particles, along a direction perpendicular to the square.

What is the distance (in cm) from the point particle with mass 2m to the center of mass of this system if d = 12 cm and m = 0.01 kg?

Explanation / Answer

For simplification , let us assume four masses as a combined mass of 4m and is located at center of square as center of mass of four masses is at center of square.

So for center of mass,

Distance of center of mass from 2m = (m1*x1 + m2 *x2 )/(m1+m2) = (4m*2d + 0*2m)/(6m) = 8*m*d/6m

= 4*d/3 = 4*12/3 = 16 cm.

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