Newton's Law of Gravitation: Practice Problem & Solution

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Newton's Law of Gravitation. Understanding the underlying formula is key to arriving at the correct answer below:

The gravitational force between two masses \( m_1 \) and \( m_2 \) is given by Newton's law of gravitation:

\[
F = \frac{G m_1 m_2}{r^2}
\]

Let the total mass be \( M = 100 \, \text{kg} \), and split it into two parts: \( m_1 = x \) and \( m_2 = 100 - x \).

The gravitational force becomes:

\[
F = \frac{G x (100 - x)}{r^2}
\]

To maximize \( F \), we need to maximize \( x(100 - x) \), which is a quadratic function. The product \( x(100 - x) \) is maximized when \( x = 50 \).

Thus, the ratio of the two masses is:

\[
m_1 : m_2 = 50 : 50 = 1:1
\]

Therefore, the masses should be in a 1:1 ratio for the gravitational force to be maximum.