1.

A particle is projected vertically upwards with a velocity sqrt(gR), where R denotes the radius of the earth and g the acceleration due to gravity on the surface of the earth. Then the maximum height ascended by the particle is

Answer»

`R_(e )`
`2R_(e )`
`(R_(e ))/(2)`
None of these

Solution :The projected speed is less than escape speed `V_(e)=sqrt(2gR_(e))`. The BODY will not reach infinity.
At maximum height the KINETIC energy becomes ZERO.
Using conservation of energy,
`(mV^(2))/(2)-(GM_(e)m)/(R_(e))=-(GM_(e)m)/(r)`
`IMPLIES (mgR_(e))/(2)-(GM_(e)m)/(R_(e))=-(GM_(e)m)/(r)(GM_(e)=gR_(e)^(2))`
`implies(mgR_(e))/(2)-mgR_(e)=-(gR_(e)^(2)m)/(r)implies(mgR_(e))/(2)=(gR_(e)^(2)m)/(r)`
`implies r=2R_(e)(r=R_(e)+h) therefore` The height attained = `R_(e)`


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