Calculate The Time Period Of Oscillation Of A Solid Cylinder Of Length ‘l’ And Radius ‘r’ About An Axis Perpendicular To Its Axis Of Symmetry And At A Distance ‘d’ From Its Centre Of Mass, Also Calculate The Minimum Time Period.

Ans. Let us consider a solid circular cylinder of radius , length and mass . Fig. 1 If be the moment of inertia of the solid cylinder about an axis…

Continue ReadingCalculate The Time Period Of Oscillation Of A Solid Cylinder Of Length ‘l’ And Radius ‘r’ About An Axis Perpendicular To Its Axis Of Symmetry And At A Distance ‘d’ From Its Centre Of Mass, Also Calculate The Minimum Time Period.

A Rectangular Plate Having Edges Of Lengths ‘a’ And ‘b’ Respectively, Hangs Vertically From The Edge Of Length ‘a’. (i) Find The Time Period For Small Oscillations And (ii) The Length Of The Equivalent Simple Pendulum.

Ans. Let us consider a rectangular plate having edges of lengths and respectively. This rectangular plate hangs vertically from the edge of length . Let be the total mass of…

Continue ReadingA Rectangular Plate Having Edges Of Lengths ‘a’ And ‘b’ Respectively, Hangs Vertically From The Edge Of Length ‘a’. (i) Find The Time Period For Small Oscillations And (ii) The Length Of The Equivalent Simple Pendulum.

A Uniform Solid Sphere Of Radius ‘a’ And Mass ‘M’ Is Suspended Vertically Downward From A Point On Its Surface. (i) Find The Time Period For Small Oscillation, And (ii) The Length Of The Equivalent Simple Pendulum.

Ans. Let us consider a uniform solid sphere of radius and of mass is suspended vertically downward a from a point on its surface. G is the centre of gravity…

Continue ReadingA Uniform Solid Sphere Of Radius ‘a’ And Mass ‘M’ Is Suspended Vertically Downward From A Point On Its Surface. (i) Find The Time Period For Small Oscillation, And (ii) The Length Of The Equivalent Simple Pendulum.

What Is The Distance Between The Centre Of The Suspension And Centre Of Oscillation Of A Uniform Cylindrical Metal Bar Used As A Second Pendulum.

Ans. If L be the distance between the centre of suspension and centre of oscillation of the compound pendulum then the time period of oscillation of the compound pendulum is…

Continue ReadingWhat Is The Distance Between The Centre Of The Suspension And Centre Of Oscillation Of A Uniform Cylindrical Metal Bar Used As A Second Pendulum.

A Cube Of Edges ‘S’ And Mass ‘M’ Is Suspended Vertically From One Of Its Edges As The Axis Of Suspension. Find The Time Period Of Small Oscillation. What Is The Length Of Equivalent Simple Pendulum.

Ans. Fig. 1 Let us consider a cube of mass and edges is suspended from one of its edges O as shown in the Fig. 1. The length of the…

Continue ReadingA Cube Of Edges ‘S’ And Mass ‘M’ Is Suspended Vertically From One Of Its Edges As The Axis Of Suspension. Find The Time Period Of Small Oscillation. What Is The Length Of Equivalent Simple Pendulum.

Show That A Uniform Rod Of Length ‘l’ Hanging As A Compound Pendulum From A Pivot At One End Has Same Frequency For Small Oscillation As A Simple Pendulum Of Length (2l/3).

Ans. Fig. 1 The time period of the simple pendulum equivalent to a compound pendulum is given by, [ to know the derivation of the above equation (CLICK HERE) ]…

Continue ReadingShow That A Uniform Rod Of Length ‘l’ Hanging As A Compound Pendulum From A Pivot At One End Has Same Frequency For Small Oscillation As A Simple Pendulum Of Length (2l/3).