Joint Entrance Examination

Graduate Aptitude Test in Engineering

Geomatics Engineering Or Surveying

Engineering Mechanics

Hydrology

Transportation Engineering

Strength of Materials Or Solid Mechanics

Reinforced Cement Concrete

Steel Structures

Irrigation

Environmental Engineering

Engineering Mathematics

Structural Analysis

Geotechnical Engineering

Fluid Mechanics and Hydraulic Machines

General Aptitude

1

A pendulum is executing simple harmonic motion and its maximum kinetic energy is K_{1}. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K_{2}. Then :

A

$${K_2}$$ = $${{{K_1}} \over 2}$$

B

K_{2} = 2K_{1}

C

K_{2} = K_{1}

D

K_{2} = $${{{K_1}} \over 4}$$

Maximum kinetic energy at lowest point B is given by

K = mg$$\ell $$ (1 $$-$$ cos $$\theta $$)

where $$\theta $$ = angular amp.

K_{1} = mg$$\ell $$ (1 $$-$$ cos $$\theta $$)

K_{2} = mg(2$$\ell $$) (1 $$-$$ cos $$\theta $$)

K_{2} = 2K_{1}.

K = mg$$\ell $$ (1 $$-$$ cos $$\theta $$)

where $$\theta $$ = angular amp.

K

K

K

2

A travelling harmonic wave is represented by the equation y(x,t) = 10^{–3}sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the following is a correct statement about the wave ?

A

The wave is propagating along the positive x-axis with speed 100 ms^{–1}

B

The wave is propagating along the positive x-axis with speed 25 ms^{–1}

C

The wave is propagating along the negative x-axis with speed 25 ms^{–1}

D

The wave is propagating along the negative x-axis with speed 100 ms^{–1}

y = a sin($$\omega $$t + kx)

$$ \Rightarrow $$ wave is moving along $$-$$ve x-axis with speed

v = $${\omega \over K}$$ $$ \Rightarrow $$ v = $${{50} \over 2}$$ = 25m/sec

$$ \Rightarrow $$ wave is moving along $$-$$ve x-axis with speed

v = $${\omega \over K}$$ $$ \Rightarrow $$ v = $${{50} \over 2}$$ = 25m/sec

3

Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length $$\ell $$ and mass m. The rod is pivoted at its centre 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is :

A

$${1 \over {2\pi }}\sqrt {{{3k} \over m}} $$

B

$${1 \over {2\pi }}\sqrt {{{6k} \over m}} $$

C

$${1 \over {2\pi }}\sqrt {{k \over m}} $$

D

$${1 \over {2\pi }}\sqrt {{{2k} \over m}} $$

$$\tau = - 2kx{\ell \over 2}\cos \theta $$

$$ \Rightarrow $$ $$\tau = \left( {{{K{\ell ^2}} \over 2}} \right)\theta = - C\theta $$

$$ \Rightarrow $$ $$f = {1 \over {2\pi }}\sqrt {{C \over 1}} = {1 \over {2\pi }}\sqrt {{{{{K{\ell ^2}} \over 2}} \over {{{M{\ell ^2}} \over {12}}}}} $$

$$ \Rightarrow $$ $$f = {1 \over {2\pi }}\sqrt {{{6K} \over M}} $$

4

A simple harmonic motion is represented by :

y = 5 (sin 3 $$\pi $$ t + $$\sqrt 3 $$ cos 3 $$\pi $$t) cm

The amplitude and time period of the motion are :

y = 5 (sin 3 $$\pi $$ t + $$\sqrt 3 $$ cos 3 $$\pi $$t) cm

The amplitude and time period of the motion are :

A

10 cm, $${3 \over 2}$$ s

B

5 cm, $${2 \over 3}$$ s

C

5 cm, $${3 \over 2}$$ s

D

10 cm, $${2 \over 3}$$ s

y = 5[sin(3$$\pi $$t) + $$\sqrt 3 $$cos(3$$\pi $$t)]

= 10sin $$\left( {3\pi t + {\pi \over 3}} \right)$$

Amplitude = 10 cm

T = $${{2\pi } \over w}$$ = $${{2\pi } \over {3\pi }}$$ = $${2 \over 3}$$ sec

Number in Brackets after Paper Name Indicates No of Questions

AIEEE 2002 (3) *keyboard_arrow_right*

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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*

Electrostatics *keyboard_arrow_right*

Current Electricity *keyboard_arrow_right*

Magnetics *keyboard_arrow_right*

Alternating Current and Electromagnetic Induction *keyboard_arrow_right*

Ray & Wave Optics *keyboard_arrow_right*

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*