Question

If pressure P of a gas is given in term of't'and distance x as P=A sin bt+B sin ct then​

Answer 1

Your answer is in the attachment hope it helps you :)

Answer 2

COMPLETE QUESTION

If pressure P of a gas is given in term of't'and distance x as P=A sin bt+B sin cx then-

(A)dimension of AB are same as bc

(B)Dimensions of A is ML-¹

(C)Dimension of A and B are same

(D)Dimension of b and c are same

ANSWER

The correct answer is option (c) Dimension of A and B are same

GIVEN

Pressure of the gas represented as;

P = A sin bt+B sin cx.

TO FIND

Which of the options are correct.

SOLUTION

We can simply solve the above problem as follows-

We know that,

Dimension of pressure = M¹L-¹T-².

Dimensions of b and c.

Since the function of trigonometry are angles. And angle is dimensionless.

[bt] = M⁰L⁰T ⁰

[bT¹] = M⁰L⁰T⁰

b = T⁻¹

Similarly,

[cx] = [M⁰L⁰T⁰]

[cL¹] = [M⁰L⁰T⁰]

c = L⁻¹

Since dimensions of b and c are not equal, option (d) is incorrect.

According to the principles of homogeneity

Dimensions of A and B is equal to the dimension of pressure.

So,

[A] = [M¹L⁻¹T⁻²]

Since, Dimension of A is not ML⁻¹ , Option (b) is incorrect

[B] = [M¹L⁻¹T⁻²]

Since, [A] = B] = [M¹L⁻¹T⁻²]

Hence, Option (c) is correct.

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