Question

The escape velocity from earth is `v_(e)`. A body is projected with velocity `2v_(e)`. With what constant velocity will it move in the inter planetary space ?
A. `v_(e)`
B. `sqrt(2)v_(e)`
C. `sqrt(3)v_(e)`
D. `sqrt(5)v_(e)`

Answer 1

Correct Answer - C
`U_(i)+K_(i)=U_(f)+K_(f)`
`rArr-(GMm)/(R)+(1)/(2)m(2v_(e))^(2)=0+(1)/(2)mv^(2)`
or `-(GM)/(R)+2v_(e)^(2)=(1)/(2)v^(2)`
or `-(2GM)/(R)+(8GM)/(R)=v^(2)`
or `v=sqrt((6GM)/(R))=sqrt(3((2GM)/(R)))=sqrt(3(2gR))=sqrt(3)v_(e)`.