Question

a point object of mass m is kept at (a,0) along x axis.what mass should be kept at (-3a,0),so that center of mass lies at origin?

answer=m/3

Answer 1

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Answer 2

Answer:

The mass that should be kept at (-3,0) is $\frac{m}{3}$.

Explanation:

$X_{cm} =\frac{m_{1}x_{1} +m_{2}x_{2} +........+m_{n}x_{n} }{n} \\X_{cm}=0$Since the center of mass lies at the origin.

Hence:

$0=\frac{m*a+x*(-3a)}{2}$

On solving, we get x=  $\frac{m}{3}$ which is the value of that mass which has to be kept at (-3a,0)

What is the center of gravity?

The center of gravity is a position defined relative to an object or system of objects. It is the average position of all parts of the system, weighted by their weight.

For example, the center of gravity of a uniform disk shape would be at its center. Sometimes the center of gravity does not fall anywhere on the object. For example, the center of gravity of a ring is in its center, where there is no material.

What is useful about the center of gravity?

The interesting thing about the center of gravity of an object or system is that it is the point where any uniform force acts on the object. This is useful because it makes it easier to solve mechanical problems where we need to describe the motion of oddly shaped objects and complicated systems.

For calculation purposes, we can treat an oddly shaped object as if all its mass were concentrated in a small object located at the center of the mass.

If we push on a rigid object at its center of gravity, then the object will always move as if it were a point mass. If an object is subjected to an unbalanced force at some other point, it will begin to rotate about the center of mass.

How can we find the center of gravity of any object or system?

In general, the centroid can be found by vector summing the weighted position vectors that point to the centroid of each object in the system.

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