KVPY SX SB Exam 2015 Question Paper

Question : 98 of 120

Marks: +1, -0

An object is propelled vertically to a maximum height of 4R from the surface of a planet of radius R and mass M. The speed of object when it returns to the surface of the planet is -

$2√{{2GM}/{5R}}$
$√{{ GM}/{2R}}$
$√{{ 3GM}/{2R}}$
$√{{ GM}/{5R}}$

Validate

Solution:

Using energy conservation

-{GMM}/R+1/2mV^2=-{GMM}/{5R}

V=2√{{2GM}/{5R}}

V is the velocity by which object is projected. When object return to earth its speed will be V.

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