Given below are two statements:
Statement-1: The gravitational potential energy of a system of two masses $m_{1}$ and $m_{2}$ separated by a distance $r$ is always negative.
Statement-2: The escape velocity from the surface of a planet depends on the mass of the object being projected.

Question

Given below are two statements:

Statement-1: The gravitational potential energy of a system of two masses $m_{1}$ and $m_{2}$ separated by a distance $r$ is always negative.

Statement-2: The escape velocity from the surface of a planet depends on the mass of the object being projected.

TestHub · Accepted Answer

Statement-1: The gravitational potential energy of a system of two masses is given by $U = - G \frac{m _{1} m _{2}}{r}$ . Since $G, m_{1}, m_{2}, r$ are all positive quantities, $U$ is always negative. Thus, Statement-1 is true.

Statement-2: The escape velocity from the surface of a planet of mass $M$ and radius $R$ is given by $v_{e} = \frac{2 GM}{R}$ . This expression does not depend on the mass of the object being projected. Thus, Statement-2 is false.

Physics - Gravitation Question with Solution | TestHub

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