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A physical quantity x depends on quantities y and z as follows; x= Ay+BtanCz, where A, B, and C are constants. Which of the following do not have the same dimensions
- a)x and B
- b)c and z⁻1
- c)y and B/A
- d)x and A
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A physical quantity x depends on quantities y and z as follows; x= Ay+...
Explanation:
To determine which of the given options do not have the same dimensions, we need to determine the dimensions of each quantity in the given equation.
Let's break down the given equation:
x= Ay BtanCz
- A, B, and C are constants.
- y and z are quantities that have not been defined.
We can assume that y and z have some physical dimensions, let's say [Y] and [Z], respectively.
Using the trigonometric identity, tanθ = sinθ/cosθ, we can rewrite the equation as:
x = Ay B(sinCz/cosCz)
We can simplify this equation as follows:
- x has dimensions [X]
- Ay has dimensions [X]/[B] = [A][Y]
- sinCz has no dimensions (since it's a ratio of two lengths)
- cosCz has no dimensions (since it's a ratio of two lengths)
- Therefore, B(sinCz/cosCz) has dimensions [B]
- Overall, we can say that the dimensions of x are [A][Y][B].
Now, let's consider each option:
a) x and B have the same dimensions - False
- We just showed that x has dimensions [A][Y][B], while B has dimensions [B].
b) c and z1 have the same dimensions - True
- c and z are not defined, so we cannot determine their dimensions.
- However, since z1 is not mentioned in the original equation, we can assume that it has no dimensions.
c) y and B/A have the same dimensions - True
- Ay has dimensions [A][Y], and B has dimensions [B].
- Therefore, B/A has dimensions [B]/[A].
- Since x has dimensions [A][Y][B], we can say that y and B/A have the same dimensions.
d) x and A have the same dimensions - False
- We just showed that x has dimensions [A][Y][B], while A has dimensions [A].
Therefore, the correct answer is option 'D': x and A do not have the same dimensions.
To determine which of the given options do not have the same dimensions, we need to determine the dimensions of each quantity in the given equation.
Let's break down the given equation:
x= Ay BtanCz
- A, B, and C are constants.
- y and z are quantities that have not been defined.
We can assume that y and z have some physical dimensions, let's say [Y] and [Z], respectively.
Using the trigonometric identity, tanθ = sinθ/cosθ, we can rewrite the equation as:
x = Ay B(sinCz/cosCz)
We can simplify this equation as follows:
- x has dimensions [X]
- Ay has dimensions [X]/[B] = [A][Y]
- sinCz has no dimensions (since it's a ratio of two lengths)
- cosCz has no dimensions (since it's a ratio of two lengths)
- Therefore, B(sinCz/cosCz) has dimensions [B]
- Overall, we can say that the dimensions of x are [A][Y][B].
Now, let's consider each option:
a) x and B have the same dimensions - False
- We just showed that x has dimensions [A][Y][B], while B has dimensions [B].
b) c and z1 have the same dimensions - True
- c and z are not defined, so we cannot determine their dimensions.
- However, since z1 is not mentioned in the original equation, we can assume that it has no dimensions.
c) y and B/A have the same dimensions - True
- Ay has dimensions [A][Y], and B has dimensions [B].
- Therefore, B/A has dimensions [B]/[A].
- Since x has dimensions [A][Y][B], we can say that y and B/A have the same dimensions.
d) x and A have the same dimensions - False
- We just showed that x has dimensions [A][Y][B], while A has dimensions [A].
Therefore, the correct answer is option 'D': x and A do not have the same dimensions.
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Community Answer
A physical quantity x depends on quantities y and z as follows; x= Ay+...
A and y in multiplication has same dimensions as that of x.. Not A alone.. Therefore d is correct option.
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A physical quantity x depends on quantities y and z as follows; x= Ay+BtanCz, where A, B, and C are constants. Which of the following do not have the same dimensionsa)x and Bb)c and z1c)y and B/Ad)x and ACorrect answer is option 'D'. Can you explain this answer?
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