Which of the pair of quantities have the same dimensional formula?

Work is equal to dot product of force and distance travelled = F . r and hence is a scalar. Torque is equal to r ×F and hence is a vector, though having same dimensions.

Simply so, which of the following pairs of quantities have the same dimensional formula?

Hence, impulse and momentum both have same dimensions i.e., [MLT−1]

Similarly, which pair of physical quantities have the same dimensions? But mostly we use only first three physical quantity i.e. Mass, Length, Time. Dimension represents the powers of fundamental physical quantities for example [MaLbTc] where a, b, c are dimensions. Here work and energy have the same unit, so that the dimensional formula is also the same.

Beside this, which quantities have the same dimensions?

Note: The dimension of quantities which are interchangeable into one another have exactly the same dimension. For example, energy can transform from one form to another. So each type of energy whether it is kinetic energy or nuclear energy, they all have the same dimension.

Which of the following has same dimensional formula?

Therefore, impulse and momentum have the same dimensional formula.

Related Question Answers

What is the dimensional formula of work?

Notes: The dimensional formula of work done is M¹ L² T^-². Work is said to be done by a force when the body is displaced actually through some distance in the direction of applied force. The S.I unit of Work is joule.

What is the dimensional formula of torque?

The SI unit for torque is Newton- meter as we know that the unit of force is newton which is equal to Force=mass×acceleration. The SI unit of mass is Kilogram and acceleration is meter/sec2. Hence the dimensional formula of torque is ML2T−2.

What is the dimensional formula of energy?

Or, E = [M] × [L¹ T^-¹]² = M¹ L² T^-². Therefore, energy is dimensionally represented as M¹ L² T^-².

Which is dimensionless quantity?

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of the unit one (or 1), which is not explicitly shown.

Which of the following is dimensional constant?

Gravitational constant also known as universal gravitational constant has a symbol G and has a dimension [M−1L3T−2] while others are dimensionless constant.

What is the dimensional formula of gravitational constant?

Or, G = [M¹ L¹ T^-²] × [L]² × [M]^-² = [M^-¹ L³ T^-²]. Therefore, the gravitational constant is dimensionally represented as M^-¹ L³ T^-².

Which of the following is a derived unit?

Examples of derived quantities and units

Name	Symbol	Expression in terms of SI base units
joule second	J⋅s	m²⋅kg⋅s⁻¹
joule per kilogram	J/kg	m²⋅s⁻²
joule per cubic metre	J/m³	m⁻¹⋅kg⋅s⁻²
newton per metre	N/m = J/m²	kg⋅s⁻²

Is work and energy has same dimensional formula?

Answer. Answer: work is the dot product of force and displacement along force. here we can see of work and energy have same dimensional formula.

Can a quantity have dimensions but no units?

No a quantity having dimension must have some units of its measurement.

What is the dimensional formula of radius?

[2πr]=[2]⋅[π]⋅[r]=1⋅1⋅L=L, since the constants 2 and π are both dimensionless and the radius r is a length. We see that 2πr has the dimension of length, which means it cannot possibly be an area.

What is dimensional constant?

Those constant which have dimension but constant value called dimensional constants, example of these constant like gravitational constant, electric field constant etc there are many dimension constants .

Can two different physical quantities have same dimensions?

Answer Expert Verified

In general, if the dimensions are same, the quantities do represent the same physical content. Like work and energy have the same dimensions and represent inter-convertible quantity. These two quantities represent the same quantity - same meaning and content.

What are the limitations of dimensional analysis?

Mention any two limitations of dimensional analysis.

This method does not tell us how to determine the proportionality constant value.
The method cannot be considered to derive composite relations.
A formula containing trigonometric function, exponential function, and logarithmic function can not derive from it.

What is the dimension of surface tension?

Surface Tension (T) = Force × Length^-¹. Or, T = [M¹ L¹ T^-²] × [L^-¹] = M¹ T^-². Therefore, surface tension is dimensionally represented as M¹ T^-².

Which pair does not have equal dimensions?

From the above data, only Force and Impulse does not have equal dimensions.

Does momentum and impulse have same dimensions?

Impulse has the same units and dimensions (M L T⁻¹) as momentum. In the International System of Units, these are kg⋅m/s = N⋅s.

Which pair of physical quantities does not have the same dimensional formula?

Answer Expert Verified

Why current is not a derived quantity?

Whether they are electrons (and usually, they are) or protons (even inside the nucleus) charges are always in motion. So, if charges are always in motion, and moving charges is current, then current could not be a derived unit, but simply a FQ by itself. The modern textbooks list current as the a FQ.

Does torque and work have same dimensions?

Torque has the dimension of force times distance, symbolically L²MT⁻². Although those fundamental dimensions are the same as that for energy or work, official SI literature suggests using the unit newton metre (N⋅m) and never the joule.

Does stress and strain have same dimension?

Stress. Hint: All physical quantities can be derived from the base quantities. In order to find a physical quantity that has some dimensions as that of strain, use elimination method by converting each given option into the fundamental quantities. Hence it will have the same dimensions as that of force.

Are all constants dimensionless?

All constants are dimensionless.

Which of the following is a dimensional variable?

Dimensional variables are those physical quantities which have dimensions of the form [M^a L^b T^c]… {where,M,L,T are fundamental physical quantities which are Mass,Length and Time respectively.

Does tension and surface tension have same dimension?

a) Tension and surface tension. Since tension is a type of force, it will also have the same dimensional formula as the dimensional formula of force i.e. [MLT-2].

Which of the following is dimensional formula for force?

Dimensional formula of force is = [M1 L1 T-2] Dimensional equation of force is [force] = [M1 L1 T-2] As discussed above you can find the dimensions of any given physical quantities.

What is the unit of velocity gradient?

The SI Unit of the Velocity gradient is 1/sec= per second. In fluid mechanics and also the continuum mechanics, the velocity gradient describes the velocity of the fluid that changes between different points. The SI Unit is Kelvin per meter (k/m).