A body is projected vertically upwards from the surface of the Earth so as to reach a height equal to the radius of the Earth. Neglecting resistance due to it, calculate the initial speed which should be imparted to the body. Mass of Earth `= 5.98 xx 10^(24) kg`, Radius of Earth `= 6400 km`, `G = 6.67 xx 10^(-11) Nm^(2) kg^(-2)`.

A body is projected vertically upwards from the surface of the Earth s

1.	A body is projected vertically upwards from the surface of the Earth so as to reach a height equal to the radius of the Earth. Neglecting resistance due to it, calculate the initial speed which should be imparted to the body. Mass of Earth `= 5.98 xx 10^(24) kg`, Radius of Earth `= 6400 km`, `G = 6.67 xx 10^(-11) Nm^(2) kg^(-2)`.
Answer» According to law of conservation of mechanical energy, `-(GM m)/(R ) + (1)/(2) m upsilon^(2) = -(GM m)/((R + R)) = - (GM m)/(2R)` `(1)/(2) m upsilon^(2) = (GM m)/(R ) [1 - (1)/(2)] = (GM m)/(2R)` or `upsilon = sqrt((GM)/(R ))`

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A body is projected vertically upwards from the surface of the Earth so as to reach a height equal to the radius of the Earth. Neglecting resistance due to it, calculate the initial speed which should be imparted to the body. Mass of Earth `= 5.98 xx 10^(24) kg`, Radius of Earth `= 6400 km`, `G = 6.67 xx 10^(-11) Nm^(2) kg^(-2)`.
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