Match the following columns.A. Potential ener | vedclass

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(A) The potential energy $(U)$ of a satellite at a distance $r$ from the center of the Earth is given by $U = -\frac{GMm}{r}$. Since the gravitational

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$A-II, B-II, C-I, D-III$

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(A) The potential energy $(U)$ of a satellite at a distance $r$ from the center of the Earth is given by $U = -\frac{GMm}{r}$. Since the gravitational force is attractive,the potential energy is always negative.The kinetic energy $(K)$ of a satellite is given by $K = \frac{GMm}{2r}$. Since $G, M, m,$ and $r$ are all positive,the kinetic energy is always positive.The total energy $(TE)$ of the satellite is the sum of its kinetic and potential energies:$TE = K + U = \frac{GMm}{2r} - \frac{GMm}{r} = -\frac{GMm}{2r}$.Thus,the total energy is always negative.The gravitational potential energy of a satellite at infinity $(r = \infty)$ is:$U = -\frac{GMm}{\infty} = 0$.Comparing these results with the given columns:$A$ (Potential energy) $\rightarrow II$ (Negative)$B$ (Total energy) $\rightarrow II$ (Negative)$C$ (Kinetic energy) $\rightarrow I$ (Positive)$D$ (Potential energy at infinity) $\rightarrow III$ (Zero)The correct matching is $A-II, B-II, C-I, D-III$.

$A$. Potential energy of satellite	$I$. Positive
$B$. Total energy of satellite	$II$. Negative
$C$. Kinetic energy of satellite	$III$. Zero
$D$. Gravitational potential energy of satellite at infinity	$IV$. Infinity

Match the following columns.
$A$. Potential energy of satellite $I$. Positive
$B$. Total energy of satellite $II$. Negative
$C$. Kinetic energy of satellite $III$. Zero
$D$. Gravitational potential energy of satellite at infinity $IV$. Infinity

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Match the following columns.$A$. Potential energy of satellite$I$. Positive$B$. Total energy of satellite$II$. Negative$C$. Kinetic energy of satellite$III$. Zero$D$. Gravitational potential energy of satellite at infinity$IV$. Infinity