Question

A, B, C and D are all dimensionally different. Then which of the following must be inconsistent? a)AB + CD; b)e ^ (AB) + sin(CD); c)log (A/B) ^ (C/D); d)A/B - C/D​

Answer 1

Option (D) is the correct answer

d) $\frac{A}{B} -\frac{C}{D}$

Explanation:

• A, B, C, and D are all dimensionally different.

• Dimensions play important role in physics.

• Various quantities and factors have various dimensions.

• Dimensions of the main fundamental quantities are M for mass while L for length, T for time, K for temperature, while A for the current.

• Dimensional analysis is very useful in solving various problems and also in checking for the validity of the options.
• The equation we have is $AD=Cln(BD)$ the logarithm function should not have any dimension.
• Product of two physical quantities and the dimension of any one quantity is the inverse of the dimension of another quantity then that product will be dimensionless.

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Answer 2

Answer:

Option (D) is the correct answer.

$d) \frac{A}{B} - \frac{C}{D}$

Explanation:

• A, B, C and D are all dimensionally different.

• Dimensional Analysis play an important role in physics.

• Different quantities and factors have different dimensions.

• The dimensions of the most important fundamental quantities are $M$ for mass,$L$ for length, $T$ for time, $K$ for temperature and $A$ for  current.

• Dimensional analysis is very useful to solve various problems and also to check the validity of  options.The equation we have is $AD = C ln(BD)$, the logarithmic function must have no dimensions.

• The product of two physical quantities and the dimension of any  quantity is the inverse of the dimension of another quantity, so the product is dimensionless.

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