Question

# ESCAPE SPEEDThe escape speed of a body on the earth's surface is 11.2 km s−1. 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 22.4√2kms−1Let 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, 12mu2−GMEmRE=12mv2−0Where m and ME masses of the body and earth respectively and RE is the radius of the earth.or v2=u2−2GMEREv2=u2=v2ev=√u2−v2e=√(3ve)2−v2e(∵ve=√2GMERE)=√8ve=11.2√8kms−1=22.4√2kms−1

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