# Classical Mechanics-Rigid Body Dynamics [Optionals IAS Mains Physics]: Questions 1 - 6 of 14

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## Question 1

Rigid Body Dynamics
Inertia Tensor

Appeared in Year: 2015

### Describe in Detail

Essay▾

Show that the moment of inertia of a circular disc of mass M and radius R about an axis passing through its centre and perpendicular to its plane is . (15 Marks)

### Explanation

• Consider a circular disc of mass ‘M’ and radius ‘R’ . Let us take an axis AB perpendicular to the plane of the disc and passing through center, about which moment of inertia is to be determined. Let us divide the disc into large number of elementary concentric circular rings. Consider any one of such ring of radius and thickness .
• Here, mass of the…

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## Question 2

Rigid Body Dynamics
Euler's Equation of Motion of a Rigid Body

Appeared in Year: 2015

### Describe in Detail

Essay▾

Using Poiseuille՚s formula, show that the volume of a liquid of viscosity coefficient passing per second through a series of two capillary tubes of lengths and having radii is obtained as where p is the effective pressure difference across the series. (15 Marks)

### Explanation

• Let two capillaries A and B, of lengths and radii respectively be connected in series, as shown in figure and let a liquid of coefficient of viscosity flow through them in steady or streamline motion. Then, since two liquids are incompressible, the same volume of liquid that passes through capillary A, in a given time also passes through capilla…

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## Question 3

Rigid Body Dynamics
Euler's Equation of Motion of a Rigid Body
Edit

Appeared in Year: 2015

### Describe in Detail

Essay▾

Define coefficient of viscosity and kinematic viscosity of a fade. What are poise and stokes? (10 Marks)

### Explanation

• If F is the external force applied to plate P to maintain a laminar streamline flow of the liquid and v, the velocity of the uppermost layer, distant z from the lowermost or stationary layer, we have tangential or shearing stress applied = where A is the surface area of the layer.
• Newton found that the shear strain is a function of the shearing st…

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## Question 4

Rigid Body Dynamics
Euler's Equation of Motion of a Rigid Body

Appeared in Year: 2016

### Describe in Detail

Essay▾

Show that the Young՚s modulus , modulus of rigidity and Poisson՚s ratio are related by the equation .

### Explanation

Let the upper face ABEG of a cube of each edge be sheared through an angle under a tangential force applied to it, as shown in Fig (1) , such that displacement AA ‘= BB’ = , with diagonal DB increased to DB ‘and diagonal AC shortened to A’ C. Then clearly, tangential stress applied , say and shear strain produced . Therefore the modulus of rigid…

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## Question 5

Rigid Body Dynamics
Principal Moments of Inertia

Appeared in Year: 2012

### Describe in Detail

Essay▾

Calculate the moment of inertia of a solid cone of mass height vertical half angle and radius of its base about an axis passing through its vertex and parallel to its base.

### Explanation

Considering the disc at a distance from the vertex of the cone, we have its M. I about its

Its M. I about the parallel axis distance from it

Hence M. I of the entire cone about the axis parallel to its base is given by

Or, substituting the value of we have M. I of the about the axis i.e..

## Question 6

Rigid Body Dynamics
Euler's Equation of Motion of a Rigid Body

Appeared in Year: 2016

### Describe in Detail

Essay▾

A horizontal pipe of non – uniform bore has water flowing through it such that the velocity of flow is at a point where the pressure is of mercury column. What is the pressure at a point where the velocity of flow is ? Take and density of water .

### Explanation

Here of mercury column , , d

In accordance with Bernoulli՚s equation,

Where is the pressure at the second point.

Or

So that

Or

Whence,

of mercury column.

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