Question

If a physical quantity (Y) depends on resistance (R) and time (1) as Y = R24. then dimensional formula of Y is​

Answer 1

If a physical quantity (Y) depends on resistance (R) and time (1) as Y = R24 are :

Physical quantity :

• Any number that is used to describe a physical phenomenon quantitatively is called a physical quantity.
• It consists of a precise numerical value and a unit.
• Physical quantity can be categorized into 2 types.
• Base quantity and  derived quantity {Quantity} = {Numerical value × Unit}.

Resistance (R) :

• It is a property of a material used for describing the opposition provided to the flow of current.
• The higher the resistance provided by a material, the lower the flow of electrons or current through the material.
• SI unit of resistance is Ohm ( Ω).

Time :

• The time command runs the specified program command with the given arguments.
• When command finishes, time writes a message to standard error giving timing statistics about this program run.

Dimensional formula of physical quantity :

• The dimensional formula of physical quantity is [M a L b T c ].
• Then, that physical quantity is 1) spring constant, if a =1, b = 1, and c = –2 2) surface tension, if a =1, b =1, and c = –2.

Answer 2

Explanation:

The dimensions of μ are given by:

A

2

N

=

A

2

MLT

−2

The dimensions of ϵ are M

−1

L

−3

T

4

A

2

.

Similarly, the dimensions of resistance are given by ML

2

T

−3

A

−2

Dividing the 2 quanitities, the dimensions of

ϵ

μ

are M

2

L

4

T

−6

A

−4

On comparing, these are also the dimensions of R

2

.