Question

A body is projected vertically from the surface of the earth of radius 'R' with velocity equal to half of the escape velocity. The maximum height reached by the body is ______.

विकल्प

• `"R"/5`

• `"R"/3`

• `"R"/2`

• `"R"/4`

Answer 1

A body is projected vertically from the surface of the earth of radius 'R' with velocity equal to half of the escape velocity. The maximum height reached by the body is `underlinebb("R"/3)`.

Explanation:

According to the law of conservation of energy,

`("Total energy")_"surface" = ("Total energy")_("max height")`

`=> ("KE" + "PE")_"surface" = ("KE" + "PE")_("max height")`

`=> 1/2 "mv"^2 + (- "GMm"/"R") = 0 + (- "GMm"/("R + h"))`

Given, v = `1/2 "v"_"e" = 1/2sqrt((2"GM")/"R")`

`=> 1/2"m" [1/4 * "2GM"/"R"] - "GMm"/"R" = - "GMm"/("R + h")`

`=> 1/4 "GMm"/"R" - "GMm"/"R" = - "GMm"/"R + h"`

`=> (1 - 4)/"4R" = 1/("R + h") => 3"R" + 3"h" = 4"R"`

`=> "h" = "R"/3`