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?

A Circular Disc Of Mass ‘M’ And Radius ‘r’ Is Set Rolling On A Table. If ‘ω’ Be The Angular Velocity, Calculate Its Total Energy ‘E’.

Ans. When a circular disc of mass M and radius r rolls on a table, then its total kinetic energy E will be, = (Energy due to linear motion) +…

Continue ReadingA Circular Disc Of Mass ‘M’ And Radius ‘r’ Is Set Rolling On A Table. If ‘ω’ Be The Angular Velocity, Calculate Its Total Energy ‘E’.

Two Parallel Circular Wheels, Each Of Mass ‘M’ And Radius ‘R’ And Filled With Weightless Spokes Are Rigidly Joined Together By A Weightless Rod Of Length 2R Passing Through The Centre Of The Wheels Perpendicular To Their Planes. Calculate The Moment Of Inertia Of The Wheels About An Axis Passing Perpendicular Through The Centre Of The Rod.

Ans. Fig. 1 Here, two wheels each of mass M and radius R are rigidly connected by a weightless rod of length 2R. The moment of inertia of each wheel…

Continue ReadingTwo Parallel Circular Wheels, Each Of Mass ‘M’ And Radius ‘R’ And Filled With Weightless Spokes Are Rigidly Joined Together By A Weightless Rod Of Length 2R Passing Through The Centre Of The Wheels Perpendicular To Their Planes. Calculate The Moment Of Inertia Of The Wheels About An Axis Passing Perpendicular Through The Centre Of The Rod.

Two Particles Of Masses ‘m’ And ‘M’ Are At A Distance ‘d’ Apart. Calculate The Moment Of Inertia Of The System About An Axis Passing Through The Centre Of Mass And Perpendicular To The Line Joining The Two Masses. If ‘ν’ Be The Frequency Of Revolution, Then Also Calculate The Rotational Kinetic Energy Of The System.

Ans. Fig. 1 Here the two masses 'm' and 'M' are at a distance d apart. Let us consider, O be the centre of mass of the system of these…

Continue ReadingTwo Particles Of Masses ‘m’ And ‘M’ Are At A Distance ‘d’ Apart. Calculate The Moment Of Inertia Of The System About An Axis Passing Through The Centre Of Mass And Perpendicular To The Line Joining The Two Masses. If ‘ν’ Be The Frequency Of Revolution, Then Also Calculate The Rotational Kinetic Energy Of The System.

A Uniform Rod 2 ft Long, Weighting 5 lbs, Is Revolving 60 Times A Minute About One End. Calculate Its Moment Of Inertia And Kinetic Energy.

Ans. Here the mass of the uniform rod M=5 lbs,length of the rod is l=2 ft.The rod is rotating about one end with frequency =1 rev./sec.The angular velocity is We…

Continue ReadingA Uniform Rod 2 ft Long, Weighting 5 lbs, Is Revolving 60 Times A Minute About One End. Calculate Its Moment Of Inertia And Kinetic Energy.

Calculate The Kinetic Energy Of A Thin Rod Of Length ‘l’ And Mass ‘m’ Per Unit Length Rotating About An Axis Through The Middle Point And Perpendicular To Its Length With Angular Velocity ω.

Ans: The length of the thin rod is l and mass density i.e., mass per unit length is m. So the total mass of the rod is .The rod is…

Continue ReadingCalculate The Kinetic Energy Of A Thin Rod Of Length ‘l’ And Mass ‘m’ Per Unit Length Rotating About An Axis Through The Middle Point And Perpendicular To Its Length With Angular Velocity ω.

Two Circular Metal Discs Have The Same Mass ‘M’ And The Same Thickness ‘t’. Disc ‘1’ Has A Uniform Density, Which Is Less Than That Of The Disc ‘2’. Which Disc Has The Larger Moment Of Inertia.

Ans. For disc 1, mass and thickness are M and t respectively. Let, be the radius of the circular disc and be the uniform density of the disc. The volume…

Continue ReadingTwo Circular Metal Discs Have The Same Mass ‘M’ And The Same Thickness ‘t’. Disc ‘1’ Has A Uniform Density, Which Is Less Than That Of The Disc ‘2’. Which Disc Has The Larger Moment Of Inertia.