Question

Pick out the wrong statement from the following-
A. The SI unit of universal gravitational constant is $N{m^2}k{g^{ - 2}}$
B. The gravitational force is a conservative force.
C. The force of attraction due to a hollow spherical shell of uniform density on a point mass D inside it is zero.
D. The centripetal acceleration of a satellite is equal to acceleration due to gravity.
E. Gravitational potential energy=Gravitational potential/mass of the body

Answer 1

Hint: Recall the relationship between the gravitational potential and gravitational potential energy which is \[U = V \times m\] where U= gravitational potential energy, V= gravitational potential and m=mass of the body.
Gravitational force doesn’t depend on the path between two bodies, which suggests that it is a conservative force.
Units of gravitational constant can be derived from Newton's law of gravitation.

Explanation:
Since from gravitational law we have-
$
  F = \dfrac{{G{m_1}{m_2}}}{{{r^2}}} \\
   \Rightarrow G = \dfrac{{F{r^2}}}{{{m_1}{m_2}}} \\
$
So the units of G is $\dfrac{{N{m^2}}}{{K{g^2}}} = $$N{m^2}k{g^{ - 2}}$.
Hence this statement is true.
The gravitational force is a conservative force as it doesn’t depend on the path followed by the two bodies. Therefore this is a correct statement.
The force of attraction due to a hollow spherical shell of uniform density on a point mass inside it is zero, this statement is also correct as Gravitational force is independent of the intervening medium.
The centripetal acceleration of a satellite is equal to acceleration due to gravity.
This is a true statement as centripetal acceleration of a satellite is equal to the acceleration due to gravity.
The gravitation potential is given by-
$V = \dfrac{{ - GM}}{r}$
Whereas the gravitational potential energy is given by-
$U = - \dfrac{{GMm}}{r}$
Hence this is a false statement. Therefore option (E) is the correct answer.

Note: Never confuse the relationship between the gravitational potential energy and gravitational potential. Always remember that \[U = V \times m\].