Home
Class 11
PHYSICS
Point masses m(1) and m(2) are placed at...

Point masses `m_(1) and m_(2)` are placed at the opposite ends of a rigid rod of length `L`, and negligible mass. The rod is to be set rotating about an axis perpendicualr 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 `omega_(0)` is minimum, is given by :

A

`x= (m_(1))/(m_(2))L`

B

`x= (m_(2))/(m_(1))L`

C

`x= (m_(2)L)/(m_(1) + m_(2))`

D

`x= (m_(1)L)/(m_(1) + m_(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
`K.E.= (1)/(2) I omega_(0)^(2)`
I is min. about the centre of mass
So, `(m_(1)) (x)= (m_(2)) (L-x) rArr x= (m_(2) L)/(m_(1) + m_(2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Point masses m_(1) and m_(2) are placed at the ends of a rigid rod of length L and negligible mass. The rod is to be set rotating about an axis perpendicular to its length. Locate a point on the rod through which the axis of rotation should pass in order that the work required to set the rod rotating with angular velocity omega_(0) is minimum.

Two point masses of 0.3 kg and 0.7kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

A rod is rotating with angular velocity omega about axis AB. Find costheta .

Two point masses A of mass M and B of mass of 4M are fixed at the ends of a rod of length l and of negligible mass. The rod is set rotation about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum when the distance of axis of rotation from the mass A is at

Two point masses m and 4m are connected by a light rigid rod of length l at the opposite ends. Moment of inertia of the system about an axis perpendicular to the length and passing through the centre of mass is

A rod of length l and mass m is capable of rotating freely about an axis passing through a hole at the end. The period of oscillation of this physical pendulum is

Two uniform solid of masses m_(1) and m_(2) and radii r_(1) and r_(2) respectively, are connected at the ends of a uniform rod of length l and mass m . Find the moment of inertia of the system about an axis perpendicular to the rod and passing through a point at a distance of a from the centre of mass of the rod as shown in figure.

Two bodies of mass 1 kg and 2 kg are attached to the ends of a 2 metre long weight less rod . This system is rotating about an axis passing through middle point of rod . Calculate M. I of system .