X and Y are two points at respective distances R and 2 R from the centre of Earth, where R is greater than the radius of Earth. The gravitational potential at X is -800 kJ kg -1. When a 1 kg mass is taken from X to Y, the work done on the mass is

Question

X and Y are two points at respective distances R and 2 R from the centre of Earth, where R is greater than the radius of Earth. The gravitational potential at X is -800 kJ kg -1. When a 1 kg mass is taken from X to Y, the work done on the mass is (A) 400 kJ (B) 200 kJ (C) -200 kJ (D) 80 kJ

Tardigrade Admin · Accepted Answer

VY-VX=[(-G M/(2 R))]-[(-G M/R)] ⇒ Δ V=(G M/2 R) Here, VX=-((G M/R))=-800 kJ kg -1 ⇒ Δ V=(800/2)=400 kJ / kg W ex =m Δ V=(1 kg )(400 kJ kg -1)=400 kJ

Q. $X$ and $Y$ are two points at respective distances $R$ and $2 R$ from the centre of Earth, where $R$ is greater than the radius of Earth. The gravitational potential at $X$ is $- 800$ $k J k g^{- 1}$ . When a $1 k g$ mass is taken from $X$ to $Y$ , the work done on the mass is

400 kJ

200 kJ

-200 kJ

80 kJ

$V_{Y} - V_{X} = [\frac{- GM}{( 2 R )}] - [\frac{- GM}{R}]$
$\Rightarrow Δ V = \frac{GM}{2 R}$
Here, $V_{X} = - (\frac{GM}{R}) = - 800 k J k g^{- 1}$
$\Rightarrow Δ V = \frac{800}{2} = 400 k J / k g$
$W_{e x} = m Δ V = (1 k g) (400 k J k g^{- 1}) = 400 k J$

Q. X and Y are two points at respective distances R and 2R from the centre of Earth, where R is greater than the radius of Earth. The gravitational potential at X is −800 kJkg−1. When a 1kg mass is taken from X to Y, the work done on the mass is