Joint Entrance Examination

Graduate Aptitude Test in Engineering

Geotechnical Engineering

Transportation Engineering

Irrigation

Engineering Mathematics

Construction Material and Management

Fluid Mechanics and Hydraulic Machines

Hydrology

Environmental Engineering

Engineering Mechanics

Structural Analysis

Reinforced Cement Concrete

Steel Structures

Geomatics Engineering Or Surveying

General Aptitude

1

A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be :

A

1 : 3

B

1 : 4

C

1 : 5

D

1 : 2

As we know,

moment of inertia about z axis

$${{\rm I}_z} = {{m{R^2}} \over 2}$$

and moment of inertia about z'

$${\rm I}_z^1 = {3 \over 2}m{R^2}$$

$$\therefore\,\,\,\,$$ $${{{{\rm I}_z}} \over {{\rm I}{'_z}}}$$ = $${{{{m{R^2}} \over 2}} \over {{3 \over 2}m{R^2}}}$$ = $${1 \over 3}$$

moment of inertia about z axis

$${{\rm I}_z} = {{m{R^2}} \over 2}$$

and moment of inertia about z'

$${\rm I}_z^1 = {3 \over 2}m{R^2}$$

$$\therefore\,\,\,\,$$ $${{{{\rm I}_z}} \over {{\rm I}{'_z}}}$$ = $${{{{m{R^2}} \over 2}} \over {{3 \over 2}m{R^2}}}$$ = $${1 \over 3}$$

2

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is $$\theta $$, thrown :

A

tan$$\theta $$ = $${1 \over {2\sqrt 3 }}$$

B

tan$$\theta $$ = $${1 \over 2}$$

C

tan$$\theta $$ = $${2 \over {\sqrt 3 }}$$

D

tan$$\theta $$ = $${1 \over 3}$$

Assume mass of each part = m

Here, $${{{C_1}R} \over {{C_1}A}} = \sin \theta $$

$$ \therefore $$ C

= $${1 \over 2}$$ sin$$\theta $$

$${{BY} \over {AB}} = \sin \theta $$

$$ \Rightarrow $$ BY = Lsin$$\theta $$

As By = MP

$$ \therefore $$ MP = Lsin$$\theta $$

$${{{C_2}M} \over {B{C_2}}}$$ = cos$$\theta $$

$$ \Rightarrow $$ C

$$ \Rightarrow $$ C

$$ \therefore $$ C

Now balancing torque about hinge paint A,

mg(C

$$ \Rightarrow $$ mg$$\left( {{L \over 2}\sin \theta } \right)$$ = mg$$\left( {{L \over 2}\cos \theta - L\sin \theta } \right)$$

$$ \Rightarrow $$ $${{\sin \theta } \over 2}$$ = $${{\cos \theta } \over 2} - $$ sin$$\theta $$

$$ \Rightarrow $$ $${{3\sin \theta } \over 2}$$ = $${{\cos \theta } \over 2}$$

$$ \Rightarrow $$ tan$$\theta $$ = $${1 \over 3}$$

3

If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :

A

$${L \over m}$$

B

$${4L \over m}$$

C

$${L \over 2m}$$

D

$${2L \over m}$$

dA = $${1 \over 2}$$ r

$$ \therefore $$ $${{dA} \over {dt}} = {1 \over 2}{r^2}{{d\theta } \over {dt}}$$

$$ \Rightarrow $$ $${{dA} \over {dt}} = {1 \over 2}{r^2}\omega $$ . . . . . (1)

We know,

angular momentum,

L = $$mvr$$

= $$m\left( {\omega r} \right)r$$

= mr

$$ \therefore $$ $$\omega $$ = $${L \over {m{r^2}}}$$ . . . . . (2)

Put value of $$\omega $$ in equation(1),

$${{dA} \over {dt}}$$ = $${1 \over 2}{r^2}$$ ($${L \over {m{r^2}}}$$)

= $${L \over {2m}}$$

4

A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30^{o} from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s^{$$-$$1}) will be (g = 10 ms^{$$-$$2})

A

$$\sqrt {{{30} \over 2}} $$

B

$$\sqrt {30} $$

C

$${{\sqrt {20} } \over 3}$$

D

$${{\sqrt {30} } \over 2}$$

When this rod move from initial position to final position then,

Gain in kinetic energy = loss in potential energy

$$ \therefore $$ $${1 \over 2}I$$$$\omega $$

$${1 \over 2}\left( {{{m{l^3}} \over 3}} \right)$$ $$\omega $$

$$ \Rightarrow $$ $$\omega $$

$$ \Rightarrow $$ $$\omega $$ = $$\sqrt {{{3g} \over {2l}}} $$

$$ \Rightarrow $$ $$\omega $$ = $$\sqrt {{{3 \times 10} \over {2 \times 0.5}}} $$

$$ \Rightarrow $$ $$\omega $$ = $$\sqrt {30} $$ rad/sec

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (5) *keyboard_arrow_right*

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Atoms and Nuclei *keyboard_arrow_right*

Electronic Devices *keyboard_arrow_right*

Communication Systems *keyboard_arrow_right*

Practical Physics *keyboard_arrow_right*

Dual Nature of Radiation *keyboard_arrow_right*

Units & Measurements *keyboard_arrow_right*

Motion *keyboard_arrow_right*

Laws of Motion *keyboard_arrow_right*

Work Power & Energy *keyboard_arrow_right*

Simple Harmonic Motion *keyboard_arrow_right*

Impulse & Momentum *keyboard_arrow_right*

Rotational Motion *keyboard_arrow_right*

Gravitation *keyboard_arrow_right*

Properties of Matter *keyboard_arrow_right*

Heat and Thermodynamics *keyboard_arrow_right*

Waves *keyboard_arrow_right*

Vector Algebra *keyboard_arrow_right*

Ray & Wave Optics *keyboard_arrow_right*

Electrostatics *keyboard_arrow_right*

Current Electricity *keyboard_arrow_right*

Magnetics *keyboard_arrow_right*

Alternating Current and Electromagnetic Induction *keyboard_arrow_right*