A small asteroid is orbiting around the sun in a circular orbit of radius r_o with speed V_0. A rocket is launched from the asteroid with speed V = \alphaV_0, where V is the speed relative to the sun. The highest value of a for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effects of other planets)

KVPY SX SB Exam 2012 Question Paper

Question : 92 of 120

Marks: +1, -0

A small asteroid is orbiting around the sun in a circular orbit of radius

r_o

with speed

V_0

. A rocket is launched from the asteroid with speed

V = αV_0

, where V is the speed relative to the sun. The highest value of a for which the rocket will remain bound to the solar system is (ignoring gravity due to the asteroid and effects of other planets)

$√2$
2
$√3$
1

Validate

Solution:

\B.\E=\GmM/{2\R}

=1/2{\m\v_0^2}

so, α = 1

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