The total mechanical energy of an object of mass m projected from surface of earth with escape speed is

Question

The total mechanical energy of an object of mass m projected from surface of earth with escape speed is (A) Zero (B) Infinite (C) -(G M m/2 R) (D) -(G M m/3 R)

Tardigrade Admin · Accepted Answer

Total mechanical energy = K.E + P.E V text escape =√(2 G M/R) ⇒ Total mechanical energy =(1/2) m × (2 G M/R)-(G M m/R) =0

Q. The total mechanical energy of an object of mass $m$ projected from surface of earth with escape speed is

Zero

Infinite

$- \frac{GM m}{2 R}$

$- \frac{GM m}{3 R}$

Total mechanical energy $=$ K.E + P.E
$V_{escape} = \frac{2 GM}{R}$
$\Rightarrow$ Total mechanical energy $= \frac{1}{2} m \times \frac{2 GM}{R} - \frac{GM m}{R}$
$= 0$

Q. The total mechanical energy of an object of mass m projected from surface of earth with escape speed is

Zero

Infinite

−2RGMm​

−3RGMm​

Total mechanical energy = K.E + P.E Vescape ​=R2GM​​ ⇒ Total mechanical energy =21​m×R2GM​−RGMm​ =0

Q. The total mechanical energy of an object of mass $m$ projected from surface of earth with escape speed is

$- \frac{GM m}{2 R}$

$- \frac{GM m}{3 R}$

Total mechanical energy $=$ K.E + P.E
$V_{escape} = \frac{2 GM}{R}$
$\Rightarrow$ Total mechanical energy $= \frac{1}{2} m \times \frac{2 GM}{R} - \frac{GM m}{R}$
$= 0$