Question

Find the dimensions of the following:

Moment of a couple
Power
Momentum
Velocity
Density

Answer 1

[AI-generated answer — Bot GPT 3.5]

The dimensions of the following physical quantities are as follows:

1. Moment of a couple: [moment of force] = [force] x [distance] = [M] x [L] = [ML^2T^-2]

2. Power: [power] = [work] / [time] = [force] x [distance] / [time] = [M] x [L^2] x [T^-3]

3. Momentum: [momentum] = [mass] x [velocity] = [M] x [L] x [T^-1]

4. Velocity: [velocity] = [distance] / [time] = [L] / [T]

5. Density: [density] = [mass] / [volume] = [M] / [L^3]

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the dimensions of the following quantities, we need to consider their respective units. Here are the dimensions for each:

1. Moment of a Couple:
The moment of a couple is a measure of the turning effect produced by two equal and opposite forces acting on a body but not on the same line. Its dimensions are:

[N × m] or [kg × m²/s²], where N represents a force in Newtons, m represents meters, and kg represents kilograms.

2. Power:
Power is the rate at which work is done or energy is transferred. Its dimensions are:

[W] or [kg × m²/s³], where W represents watts, kg represents kilograms, and m represents meters.

3. Momentum:
Momentum is a vector quantity that describes the motion of an object. Its dimensions are:

[kg × m/s], where kg represents kilograms and m/s represents meters per second.

4. Velocity:
Velocity is the rate of change of displacement. Its dimensions are:

[m/s], representing meters per second.

5. Density:
Density is defined as the mass per unit volume. Its dimensions are:

[kg/m³], representing kilograms per cubic meter.

Please note that these are the dimensions commonly used, but there may be alternative units for certain quantities depending on the context and system of units being used.