Question

A satellite revolves around a planet very close to its surface. By what maximum factor can its kinetic energy be increased suddenly, such that it revolves in orbit in the same way?

Options

• 1.5

• `sqrt2`

• 2

• 3

Answer 1

2

Explanation:

For a satellite moving in an orbit close to the planet's surface,

`"mv"^2/"R"` = mg

⇒ v² = gR .............(i)

The escape speed of the satellite, v_e = `sqrt(2"gR")`

⇒ `"v"_e^2 = 2"gR"` ............(ii)

Kinetic energy, KE = `1/2"mv"^2`

∴ `(("KE")_"e")/(("KE")) = (1/2"mv"_"e"^2)/(1/2"mv"^2) = (2"gR")/("gR") = 2` [using Eqs. (i) and (ii)]