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ESCAPE SPEED
The escape speed of a body on the earth's surface is 11.2 km s1. A body is projected with thrice of this speed. The speed of the body when it escapes the gravitational pull of the earth

A
11.2kms1
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B
22.42kms1
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C
22.42kms1
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D
22.43kms1
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Solution

The correct option is B 22.42kms1
Let v be the speed of the body when it escapes the gravitational pull of the earth and u be speed of projection of the body from the earth's surface. According to law of conservation of mechanical energy, 12mu2GMEmRE=12mv20

Where m and ME masses of the body and earth respectively and RE is the radius of the earth.

or v2=u22GMERE

v2=u2=v2e

v=u2v2e=(3ve)2v2e(ve=2GMERE)

=8ve=11.28kms1=22.42kms1

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