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 particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is -

A

$${{4\pi } \over 3}$$

B

$${3 \over 8}\pi $$

C

$${7 \over 3}\pi $$

D

$${{8\pi } \over 3}$$

$$v = \omega \sqrt {{A^2} - {x^2}} \,\,$$ . . .(1)

$$a = - {\omega ^2}x$$ . . .(2)

$$\left| v \right| = \left| a \right|$$ . . .(3)

$$\omega \sqrt {{A^2} - {x^2}} = {\omega ^2}x$$

$${A^2} - {x^2} = {\omega ^2}{x^2}$$

$${5^2} - {4^2} = {\omega ^2}\left( {{4^2}} \right)$$

$$ \Rightarrow \,\,\,3 = \omega \times 4$$

$$T = 2\pi /\omega $$

$$a = - {\omega ^2}x$$ . . .(2)

$$\left| v \right| = \left| a \right|$$ . . .(3)

$$\omega \sqrt {{A^2} - {x^2}} = {\omega ^2}x$$

$${A^2} - {x^2} = {\omega ^2}{x^2}$$

$${5^2} - {4^2} = {\omega ^2}\left( {{4^2}} \right)$$

$$ \Rightarrow \,\,\,3 = \omega \times 4$$

$$T = 2\pi /\omega $$

2

A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = Asin$${{\pi t} \over {90}}$$. The ratio of kinetic to potential energy of this particle at t = 210 s will be:

A

$${1 \over 9}$$

B

3

C

2

D

1

K = $${1 \over 2}$$m$${\omega ^2}$$A^{2}cos^{2}$$\omega $$t

U = $${1 \over 2}m{\omega ^2}$$ A^{2} sin^{2} $$\omega $$t

$${k \over U}$$ = cot^{2} $$\omega $$t = cot^{2} $${\pi \over {90}}$$(210) = $${1 \over 3}$$

Hence ratio is 3 (most appropriate)

U = $${1 \over 2}m{\omega ^2}$$ A

$${k \over U}$$ = cot

Hence ratio is 3 (most appropriate)

3

A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of 10^{–2} m. The relative change in the angular frequency of the pendulum is best given by :

A

1 rad/s

B

10^{$$-$$3} rad/s

C

10^{$$-$$1} rad/s

D

10^{$$-$$5} rad/s

Angular frequency of pendulum

$$\omega $$ = $$\sqrt {{{{g_{eff}}} \over \ell }} $$

$$ \therefore $$ $${{\Delta \omega } \over \omega }$$ = $${1 \over 2}$$ $${{\Delta {g_{eff}}} \over {{g_{eff}}}}$$

$$\Delta $$$$\omega $$ = $${1 \over 2}$$ $${{\Delta g} \over g} \times \omega $$

[$${\omega _s}$$ = angular frequency of support]

$$\Delta $$$$\omega $$ = $${1 \over 2} \times {{2A\omega _s^2} \over {100}} \times 100$$

$$\Delta \omega = {10^{ - 3}}$$ rad/sec.

$$\omega $$ = $$\sqrt {{{{g_{eff}}} \over \ell }} $$

$$ \therefore $$ $${{\Delta \omega } \over \omega }$$ = $${1 \over 2}$$ $${{\Delta {g_{eff}}} \over {{g_{eff}}}}$$

$$\Delta $$$$\omega $$ = $${1 \over 2}$$ $${{\Delta g} \over g} \times \omega $$

[$${\omega _s}$$ = angular frequency of support]

$$\Delta $$$$\omega $$ = $${1 \over 2} \times {{2A\omega _s^2} \over {100}} \times 100$$

$$\Delta \omega = {10^{ - 3}}$$ rad/sec.

4

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

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*

Dual Nature of Radiation *keyboard_arrow_right*

Atoms and Nuclei *keyboard_arrow_right*

Electronic Devices *keyboard_arrow_right*

Communication Systems *keyboard_arrow_right*

Practical Physics *keyboard_arrow_right*