If the unit of length and time is doubled then * the unit of g( acc due to gravity) will 1)halved 2) doubled

* the numerical value of g will be 1) halved 2) doubled

To tackle your question about how changes in the units of length and time affect the acceleration due to gravity (g), we need to break it down into two parts: the unit of g and its numerical value. Let's dive into each aspect step by step.

Understanding the Unit of g

The acceleration due to gravity is defined as the rate at which an object accelerates towards the Earth due to gravitational force. The standard unit for g is meters per second squared (m/s²). If we double the unit of length (from meters to, say, kilometers) and the unit of time (from seconds to minutes), we need to see how this affects the unit of g.

• Doubling the unit of length means 1 meter becomes 2 meters.
• Doubling the unit of time means 1 second becomes 2 seconds.

Now, let's analyze how this affects the unit of g:

• The formula for acceleration is given by: a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time.
• If we double the unit of length, we are effectively changing the denominator in our unit of acceleration. For instance, if we express 1 m/s² in terms of kilometers and minutes, we would convert it as follows:

1 m/s² = (1 km / (2 min)²) = 1 km / 4 min² = 0.25 km/min².

Thus, the unit of g, when expressed in the new units, is halved. Therefore, the correct answer is:

Examining the Numerical Value of g

The numerical value of g, which is approximately 9.81 m/s², is a constant that represents the acceleration due to gravity at the Earth's surface. This value does not change based on the units we use; it remains the same regardless of whether we express it in meters, kilometers, seconds, or minutes.

So, even after changing the units, the numerical value of g remains:

In summary, when we double the units of length and time, the unit of g is halved, but the numerical value of g remains constant at approximately 9.81, regardless of the units used. This illustrates an important principle in physics: while units can change, the fundamental constants of nature remain the same.