Gravitational Force on Earth Calculation

The gravitational force experienced by a body on the Earth's surface, often referred to as its weight, is directly proportional to its mass. This relationship is defined by the formula:

$ F = m \times g $

Where:

• \( F \) is the gravitational force (in Newtons, N)
• \( m \) is the mass of the body (in kilograms, kg)
• \( g \) is the acceleration due to gravity on Earth's surface (approximately 9.8 m/s², constant for this problem)

Analyzing the Change in Force

We are given that the initial gravitational force experienced by a body of mass 'm' is 'X' N. Using the formula:

$ X = m \times g $

The problem states that the mass of the body is tripled. This means the new mass, let's call it \( m_{new} \), becomes:

$ m_{new} = 3 \times m $

The acceleration due to gravity \( g \) remains constant as the body is still on the Earth's surface.

Calculating the New Gravitational Force

To find the new gravitational force (let's call it \( F_{new} \)), we use the same formula with the new mass:

$ F_{new} = m_{new} \times g $

Substitute \( m_{new} = 3m \) into the equation:

$ F_{new} = (3m) \times g $

Rearranging the terms:

$ F_{new} = 3 \times (m \times g) $

Since we know from the initial condition that \( m \times g = X \), we can substitute 'X' into the equation:

$ F_{new} = 3 \times X $

Therefore, the new gravitational force experienced by the body will be \( 3X \) N.