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Oswaal CBSE Question Bank Chapterwise For Term 2, Class 10, Science (For 2022 Exam) Oswaal CBSE Question Bank Chapterwise For Term 2, Class 10, Science (For 2022 Exam)

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1.If velocity, force and time are taken to be the fundamental quantities then find the the dimensional formula for mass.
2. Find the dimensional formula for PERMITTIVITY

For solutions and explanations
Refer

NEET / JEE PREPARATIONS - DIMENSIONAL FORMULA FOR MASS AND PERMITTIVITY This video shows how to derive dimensional formula for mass and permittivity

Dimensional Formula of Resistance =
M1 L2 T-3 I-2

Where,

M = Mass
I = Current
L = Length
T = Time

We know that

V = I*R
Therefore
R = V/ I

Also we know that
V = work done / Charge

The formula of
Work done = Force * distance

Force = mass * acceleration

Mass = M
Acceleration = distance/ time ^2

Acceleration= Length / time ^2

Distance is measured in length so we take length here

F = M L T^-2

Charge Q = Current *time
= I * T

∴ The dimensional formula of voltage = [workdone/Charge]
= Force * distance / charge
= Mass * Acceleration * distance / charge
= M L T^-2 * L * I ^-1 * T^ -1

= M L^2 T^-3 I^-1

Resistance (R) = Voltage /Current
= V*I ^-1

R = [M^1 L^2 T^-3 I^-1]*I^-1
= M^1 L ^2 T^-3 I ^-2

Therefore the DIMENSIONAL FORMULA of resistance is

M^1 L ^2 T^-3 I ^-2

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