Question

Pick out the wrong statement from the following

• A. The SI unit of universal gravitational constant is $\text{Nm}^2\text{kg}^{-2}$
• 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 inside it is zero
• D. The centripetal acceleration of the satellite is equal to acceleration due to gravity
• E. $\text{Gravitational potential energy} = \frac{\text{gravitation potential}}{\text{mass of the body}}$

Hint:

Always remember: "Potential" is like "price per kg," and "Potential Energy" is the "total cost". To get the total cost, you multiply the weight by the price!

Answer 1

Answer: (E)

Concept: This question tests basic definitions and properties within Gravitation.
• Statements A-D: These are all well-established facts.
• (A) $G = \frac{Fr^2}{m_1m_2} \rightarrow \text{Nm}^2/\text{kg}^2$.
• (B) Conservative forces do work independent of path.
• (C) Shell theorem states field inside a hollow sphere is zero.
• (D) For a satellite in orbit, the only force is gravity, providing centripetal acceleration.
• Potential vs. Energy: Gravitational Potential ($V$) is defined as the potential energy ($U$) per unit mass.

Step 1: Evaluate the mathematical definition of potential. The relationship is: \[ \text{Gravitational Potential } (V) = \frac{\text{Gravitational Potential Energy } (U)}{\text{Mass } (m)} \] Rearranging for Potential Energy ($U$): \[ \text{Gravitational Potential Energy } (U) = \text{Gravitational Potential } (V) \times \text{Mass } (m) \]

Step 2: Identify the error in statement (E). Statement (E) claims that energy is potential divided by mass. This is mathematically incorrect; it is the product of potential and mass. Therefore, statement (E) is the "wrong statement".