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 rocket is fired vertically from the earth with an acceleration of 2g, where g is the
gravitational acceleration. On an inclined plane inside the rocket, making an angle $$\theta $$ with the horizontal, a point object of mass *m* is kept. The minimum coefficient of friction $$\mu $$_{min} between the mass and the inclined surface such that the mass does not move is :

A

tan$$\theta $$

B

2tan$$\theta $$

C

3tan$$\theta $$

D

tan2$$\theta $$

Rocket is moving upward with acceleration 2g and gravitation acceleration is g downward direction.

So, acceleration experienced by the point object,

= 2g $$-$$ ($$-$$ g) = 3g

At equilibrium,

N = 3mgcos$$\theta $$

$$\mu $$N = 3mgsin$$\theta $$

$$ \Rightarrow $$ $$\mu $$ (3mgcos$$\theta $$) = 3mg sin$$\theta $$

$$ \Rightarrow $$ $$\mu $$ = tan$$\theta $$

So, acceleration experienced by the point object,

= 2g $$-$$ ($$-$$ g) = 3g

At equilibrium,

N = 3mgcos$$\theta $$

$$\mu $$N = 3mgsin$$\theta $$

$$ \Rightarrow $$ $$\mu $$ (3mgcos$$\theta $$) = 3mg sin$$\theta $$

$$ \Rightarrow $$ $$\mu $$ = tan$$\theta $$

2

A particle of mass m is acted upon by a force F given by the empirical law
F =$${R \over {{t^2}}}\,v\left( t \right).$$ If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :

A

$$\upsilon $$(t) against t^{2}

B

log $$\upsilon $$(t) against $${1 \over {{t^2}}}$$

C

log $$\upsilon $$(t) against t

D

log $$\upsilon $$(t) against $${1 \over {{t}}}$$

Given,

F = $${R \over {{t^2}}}$$ v(t)

$$ \Rightarrow $$ m $${{dv} \over {dt}}$$ = $${R \over {{t^2}}}$$ (v)

$$ \Rightarrow $$ $${{dv} \over v}$$ = $${R \over m}$$ $${{dt} \over {{t^2}}}$$

Intergrating both sides,

$$\int {{{dv} \over v} = {R \over m}\int {{{dt} \over {{t^2}}}} } $$

$$ \Rightarrow $$ lnv = $${{R \over m}}$$ $$ \times $$ $$\left( { - {1 \over t}} \right)$$ + C

$$ \Rightarrow $$ lnv = $$-$$ $${{R \over m}}$$ $$\left( {{1 \over t}} \right)$$ + C

Graph between lnv and $${{1 \over t}}$$ will be straight line curve.

F = $${R \over {{t^2}}}$$ v(t)

$$ \Rightarrow $$ m $${{dv} \over {dt}}$$ = $${R \over {{t^2}}}$$ (v)

$$ \Rightarrow $$ $${{dv} \over v}$$ = $${R \over m}$$ $${{dt} \over {{t^2}}}$$

Intergrating both sides,

$$\int {{{dv} \over v} = {R \over m}\int {{{dt} \over {{t^2}}}} } $$

$$ \Rightarrow $$ lnv = $${{R \over m}}$$ $$ \times $$ $$\left( { - {1 \over t}} \right)$$ + C

$$ \Rightarrow $$ lnv = $$-$$ $${{R \over m}}$$ $$\left( {{1 \over t}} \right)$$ + C

Graph between lnv and $${{1 \over t}}$$ will be straight line curve.

3

A conical pendulum of length 1 m makes an angle $$\theta $$ = 45^{o} w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be: (Take g = 10 ms^{−2} )

A

0.4 m/s

B

4 m/s

C

0.2 m/s

D

2 m/s

FBD of pendulum is :

$$\therefore\,\,\,$$ T sin $$\theta $$ = $${{m{v^2}} \over r}$$

T cos $$\theta $$ = mg

$$\therefore\,\,\,$$ tan $$\theta $$ = $${{{v^2}} \over {rg}}$$

$$ \Rightarrow $$$$\,\,\,$$ tan45^{o}^{} = $${{{v^2}} \over {rg}}$$

$$ \Rightarrow $$$$\,\,\,$$ v^{2} = rg

$$ \Rightarrow $$$$\,\,\,$$ v = $$\sqrt {0.4 \times 10} $$ = 2 m/s

$$\therefore\,\,\,$$ T sin $$\theta $$ = $${{m{v^2}} \over r}$$

T cos $$\theta $$ = mg

$$\therefore\,\,\,$$ tan $$\theta $$ = $${{{v^2}} \over {rg}}$$

$$ \Rightarrow $$$$\,\,\,$$ tan45

$$ \Rightarrow $$$$\,\,\,$$ v

$$ \Rightarrow $$$$\,\,\,$$ v = $$\sqrt {0.4 \times 10} $$ = 2 m/s

4

Two masses m_{1} = 5 kg and m_{2} = 10 kg, connected by an inextensible
string over a frictionless pulley, are moving as shown in the figure. The
coefficient of friction of horizontal surface is 0.15. The minimum
weight m that should be put on top of m_{2} to stop the motion is :

A

10.3 kg

B

18.3 kg

C

27.3 kg

D

43.3 kg

Moving block will stop when the friction force between m_{2} and surface is $$ \ge $$ tension force.

So condition for stopping the moving block,

$$f \ge T$$

$$ \Rightarrow \mu N \ge T$$

$$ \Rightarrow \mu \left( {m + {m_2}} \right)g \ge {m_1}g$$

When m is minimum then,

$$\mu \left( {m + {m_2}} \right)g = {m_1}g$$

$$ \Rightarrow m = {{{m_1} - \mu {m_2}} \over \mu }$$

$$ \Rightarrow m = {{5 - 0.15 \times 10} \over {0.15}}$$ = 23.33 kg

So if m $$ \ge $$ 23.33 kg then the motion will stop. From option the minimum possible m is 27.3 kg.

So condition for stopping the moving block,

$$f \ge T$$

$$ \Rightarrow \mu N \ge T$$

$$ \Rightarrow \mu \left( {m + {m_2}} \right)g \ge {m_1}g$$

When m is minimum then,

$$\mu \left( {m + {m_2}} \right)g = {m_1}g$$

$$ \Rightarrow m = {{{m_1} - \mu {m_2}} \over \mu }$$

$$ \Rightarrow m = {{5 - 0.15 \times 10} \over {0.15}}$$ = 23.33 kg

So if m $$ \ge $$ 23.33 kg then the motion will stop. From option the minimum possible m is 27.3 kg.

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*