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A man can jump over b=4m wide trench on ...

A man can jump over `b=4m` wide trench on earth. If mean density of an imaginary plent is twice that of the earth, calculate its maximum possible radius so that the he may escape from it by jumping. Given radius of earth `6400 km`.

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(6.4) km`
`R=(V^(2)sin 2 theta)/gimpliesR_(max)=(V^(2))/g`
`4=(V^(2))/gimpliesV=sqrt(4g)`
this velocity should be greater than escape velocity on that planet.
`VleVeimpliessqrt(4g)lesqrt(2g'R')`
`R'=(2g)/(g')impliesR'=2.((4/3pirhoRG))/((4/3pi(2rho)R'G))`
`R'^(2)=R=64xx10^(5)`
`R'^(2)=6.4xx10^(6)mimpliesR'sqrt(6.4)xx1000m`
`R'=sqrt(6.4)km`
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