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System of Particles and Rotational Motion

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12

Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L and negligible mass. The rod of length L and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity   is minimum is given by

D.

As two point masses m1 and m2 are placed at opposite ends of a rigid rod of length L and negligible as shown in the figure.

Total moment of inertia of the rod

I = m1x2  + m2(L-x)2

I = m1x2 + m2L2 +m2x2 - 2m2Lx

As I is minimum i.e

When I is minimum, the work done by rotating a rod will be minimum.

As two point masses m1 and m2 are placed at opposite ends of a rigid rod of length L and negligible as shown in the figure.

Total moment of inertia of the rod

I = m1x2  + m2(L-x)2

I = m1x2 + m2L2 +m2x2 - 2m2Lx

As I is minimum i.e

When I is minimum, the work done by rotating a rod will be minimum.

2889 Views

Is it necessary for centre of mass to lie within the body?

No, centre of mass needs not to lie within the body. It is not necessary that the total mass of the system be actually present at the centre.

The position of the centre of mass is calculated using the usual Newtonian type of equations of motion.
943 Views

Is it necessary that there should be matter at the centre of mass of system?

No, it is not necessary that there be matter at the centre of mass of the system.

For e.g., if two equal point masses are separated by certain distance, the centre of mass lies at the mid point of two point masses and there is no mass at that point.
730 Views

What is the need of centre of mass?

Newton’s second law of motion is strictly applicable to point masses only. To apply the Newton's law of motion to rigid bodies, the concept of centre of mass is introduced.

The concept of centre of mass of a system enables us to discuss overall motion of the system by replacing the system by an equivalent single point object.
911 Views

Define centre of mass.

Centre of mass of a body or a system of bodies is a point at which the entire mass of the body or system is supposed to be concentrated.
1449 Views

What is the significance of defining the center of mass of a system?

The motion of n particle system can be reduced to one particle motion.

An equivalent single point object would enable us to discuss the overall motion of the system.
794 Views