Question

The equation describing the motion of a particle along Y-axis is given by y=At^2-Bt^3.Find the dimension of B

Answer 1

Answer:

L T^ -3

Explanation:

Y = lenght so dimensional formula for y is L

Y= BT^3

If we replace Y with B

The equation will be like this

L / T^3

If we move the T up the answer will be L T ^-3

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Answer 2

Answer:

The correct answer to this question is

dimension of B = [ L T⁻³ ]

Explanation:

Units and Dimensions:

Five basic dimensions are used to express all the other physical quantities. They are

• Mass [M],
• Length [L],
• Time [T],
• Temperature [θ],
• Charge [q].

that is each physical quantity dimension is measured by the powers of basic dimensions.

Note:

• Terms on the LHS side and RHS side have the same dimensions
• if multiple terms are present on any side by means of addition or subtraction, each term has the same dimension only

given, the equation of a particle moving along Y-axis is y=At^2-Bt^3

here, the dimensions of y, A, and B are the same.

so, to find the dimensions of B we can follow this process

dimensions of (y) = dimensions of (BT³)

L = B × T³

B = L / T³

∴ B = [ L / T³ ]   (or)   B = [ L T⁻³ ]

hence, the dimensions of B are  [ L T⁻³ ]

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