 JEE Mains Previous Years Questions with Solutions

4.5
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1

AIEEE 2003

The time period of satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to $4$ times the previous value, the new time period will become
A
$10$ hours
B
$80$ hours
C
$40$ hours
D
$20$ hours

Explanation

According to kepler's law,

${T^2} \propto {R^3}$

$\therefore$ ${{T_1^2} \over {T_2^2}} = {{R_1^3} \over {R_2^3}}$

$\Rightarrow$ ${T_2} = {T_1}{\left( {{{{R_2}} \over {{R_1}}}} \right)^{{\raise0.5ex\hbox{3} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{2}}}} = 5 \times {\left[ {{{4R} \over R}} \right]^{{\raise0.5ex\hbox{3} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{2}}}}$

$= 5 \times {2^3} = 40\,\,$ hour
2

AIEEE 2002

Energy required to move a body of mass $m$ from an orbit of radius $2R$ to $3R$ is
A
${{GMm} \over {12{R^2}}}$
B
${{GMm} \over {3{R^2}}}$
C
${{GMm} \over {8R}}$
D
${{GMm} \over {6R}}$

Explanation

Gravitational potential energy E = $- {{GMm} \over r}$

where M = mass of earth

m = mass of body

Energy required to move a body of mass $m$ from an orbit of radius $2R$ to $3R$

$=$ (Potential energy of the Earth-mass system when mass is at distance $3R$ ) $-$ (Potential energy of the Earth-mass system when mass is at distance $2R$)

$= {{ - GMm} \over {3R}} - \left( {{{ - GMm} \over {2R}}} \right)$

$= {{ - GMm} \over {3R}} + {{GMm} \over {2R}}$

$= {{ - 2GMm + 3GMm} \over {6R}} = {{GMm} \over {6R}}$
3

AIEEE 2002

The escape velocity of a body depends upon mass as
A
${m^0}$
B
${m^1}$
C
${m^2}$
D
${m^3}$

Explanation

Escape velocity,

${v_e} = \sqrt {2gR} = \sqrt {{{2GM} \over R}} \Rightarrow {V_e}\, \propto \,{m^0}$

Where $M,R$ are the mass and radius of the planet respectively. In this expression the mass of the body $(m)$ is not present. The escape velocity is independent of the mass m or it depends on m0.

4

AIEEE 2002

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will
A
continue to move in its orbit with same velocity
B
move tangentially to the original orbit with the same velocity
C
become stationary in its orbit
D
move towards the earth

Explanation

When gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the centripetal force becomes zero. So the satellite will move tangentially to the original orbit with the same velocity as it has at the instant when gravitational force becomes zero.