Derive An Expression For The Moment Of Inertia Of A Rigid Body About Any Axis Through A Point, The Point Through Which Three Mutually Perpendicular Axes Pass.

Moment of inertia about an arbitrary axis: Let us consider, three mutually perpendicular axes OX, OY and OZ meeting at the origin O. Now we want to calculate the moment…

Continue ReadingDerive An Expression For The Moment Of Inertia Of A Rigid Body About Any Axis Through A Point, The Point Through Which Three Mutually Perpendicular Axes Pass.

A System Consists Of Three Identical Spheres Of Radius ‘r’ And Mass ‘m’ Placed With Their Centres Forming The Vertices Of An Equilateral Triangle Of Side ‘a’. Calculate The Moment Of Inertia Of The About An Axis Passing Through The Centre Of Gravity Of The System And Perpendicular To The Place Of The Centres.

Ans. Fig. 1 Three spheres of radius 'r' and mass 'm' placed with their centres at the vertices of an equilateral triangle ABC. Here G is the centre of gravity.…

Continue ReadingA System Consists Of Three Identical Spheres Of Radius ‘r’ And Mass ‘m’ Placed With Their Centres Forming The Vertices Of An Equilateral Triangle Of Side ‘a’. Calculate The Moment Of Inertia Of The About An Axis Passing Through The Centre Of Gravity Of The System And Perpendicular To The Place Of The Centres.

Centres Of Four Solid Spheres Of Diameter ‘2a’ And Mass ‘m’ Make Square Of Side ‘b’. Calculate The Moment Of Inertia Of The System About One Side Of The Square.

Ans. Four spheres, each of mass m and radius a, are placed at the corners of the square of side b, as shown in Fig.1. Fig. 1 We know that…

Continue ReadingCentres Of Four Solid Spheres Of Diameter ‘2a’ And Mass ‘m’ Make Square Of Side ‘b’. Calculate The Moment Of Inertia Of The System About One Side Of The Square.

A Cylinder Has A Mass ‘M’, Length ‘l’ And Radius ‘a’. Find The Ratio Of ‘l’ To ‘a’ If The Moment Of Inertia About An Axis Through The Centre And Perpendicular To The Length Is Minimum

Ans. Here, the mass of the cylinder is M, radius is a and length is l. If be the density of material of the cylinder, then the mass of the…

Continue ReadingA Cylinder Has A Mass ‘M’, Length ‘l’ And Radius ‘a’. Find The Ratio Of ‘l’ To ‘a’ If The Moment Of Inertia About An Axis Through The Centre And Perpendicular To The Length Is Minimum

A Solid Spherical Ball Rolls On A Table, Find The Ratio Of Its Translational And Rotational Kinetic Energies And The Total Energy Of The Spherical Ball. What Fraction Of The Total Energy Is Rotational?

Ans. Let us consider a spherical ball of radius r and mass M. If v be the linear velocity of the ball then the translational kinetic energy of the ball…

Continue ReadingA Solid Spherical Ball Rolls On A Table, Find The Ratio Of Its Translational And Rotational Kinetic Energies And The Total Energy Of The Spherical Ball. What Fraction Of The Total Energy Is Rotational?