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 satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -

A

mv^{2}

B

$${1 \over 2}$$ mv^{2}

C

$${3 \over 2}$$ mv^{2}

D

2 mv^{2}

At height r from center of earth. orbital velocity

= $$\sqrt {{{GM} \over r}} $$

$$ \therefore $$ By energy conservation

KE of 'm' + $$\left( { - {{GMm} \over r}} \right)$$ = 0 + 0

(At infinity, PE = KE = 0)

$$ \Rightarrow $$ KE of 'm' = $${{{GMm} \over r}}$$ = $${\left( {\sqrt {{{GM} \over r}} } \right)^2}$$ m = mv^{2}

= $$\sqrt {{{GM} \over r}} $$

$$ \therefore $$ By energy conservation

KE of 'm' + $$\left( { - {{GMm} \over r}} \right)$$ = 0 + 0

(At infinity, PE = KE = 0)

$$ \Rightarrow $$ KE of 'm' = $${{{GMm} \over r}}$$ = $${\left( {\sqrt {{{GM} \over r}} } \right)^2}$$ m = mv

2

Two stars of masses 3 $$ \times $$ 10^{31} kg each, and at distance 2 $$ \times $$ 10^{11} m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is - (Take Gravitational constant; G = 6.67 $$ \times $$ 10^{–11} Nm^{2} kg^{–2})

A

2.4 $$ \times $$ 10^{4} m/s

B

1.4 $$ \times $$ 10^{5} m/s

C

3.8 $$ \times $$ 10^{4} m/s

D

2.8 $$ \times $$ 10^{5} m/s

By energy convervation between 0 & $$\infty $$.

$$ - {{GMm} \over r} + {{ - GMm} \over r} + {1 \over 2}m{V^2} = 0 + 0$$

[M is mass of star m is mass of meteroite)

$$ \Rightarrow $$ v $$ = \sqrt {{{4GM} \over r}} = 2.8 \times {10^5}$$m/s

$$ - {{GMm} \over r} + {{ - GMm} \over r} + {1 \over 2}m{V^2} = 0 + 0$$

[M is mass of star m is mass of meteroite)

$$ \Rightarrow $$ v $$ = \sqrt {{{4GM} \over r}} = 2.8 \times {10^5}$$m/s

3

A satellite is revolving in a circular orbit at a height h form the earth surface, such that h < < R where R is the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is :

A

$$\sqrt {gR} \left( {\sqrt 2 - 1} \right)$$

B

$$\sqrt {2gR} $$

C

$$\sqrt {gR} $$

D

$${{\sqrt {gR} } \over 2}$$

v_{0} = $$\sqrt {g(R + h)} \approx \sqrt {gR} $$

v_{e} = $$\sqrt {2g(R + h)} \approx \sqrt {2gR} $$

$$\Delta $$v=v_{e} $$-$$ v_{0} = $$\left( {\sqrt 2 - 1} \right)\sqrt {gR} $$

v

$$\Delta $$v=v

4

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of simple pendulum on the Earth is 2 s. The period of oscillation of the same pendulum on the planet would be :

A

$${{\sqrt 3 } \over 2}$$ s

B

$${3 \over 2}$$ s

C

$${2 \over {\sqrt 3 }}$$ s

D

$$2\sqrt 3 $$ s

$$ \because $$ g = $${{GM} \over {{R^2}}}$$

$${{{g_p}} \over {{g_e}}}$$ = $${{{M_e}} \over {{M_e}}}{\left( {{{{{\mathop{\rm R}\nolimits} _e}} \over {{R_p}}}} \right)^2}$$ = 3$${\left( {{1 \over 3}} \right)^2}$$ = $${{1 \over 3}}$$

Also T $$ \propto $$ $${1 \over {\sqrt g }}$$

$$ \Rightarrow $$ $${{{T_p}} \over {{T_e}}}$$ = $$\sqrt {{{{g_e}} \over {{g_p}}}} $$ = $$\sqrt 3 $$

$$ \Rightarrow $$ T_{p} = 2$$\sqrt 3 $$ s

$${{{g_p}} \over {{g_e}}}$$ = $${{{M_e}} \over {{M_e}}}{\left( {{{{{\mathop{\rm R}\nolimits} _e}} \over {{R_p}}}} \right)^2}$$ = 3$${\left( {{1 \over 3}} \right)^2}$$ = $${{1 \over 3}}$$

Also T $$ \propto $$ $${1 \over {\sqrt g }}$$

$$ \Rightarrow $$ $${{{T_p}} \over {{T_e}}}$$ = $$\sqrt {{{{g_e}} \over {{g_p}}}} $$ = $$\sqrt 3 $$

$$ \Rightarrow $$ T

Number in Brackets after Paper Name Indicates No of Questions

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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*