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Physical quantity x depends on quantities y and z as x = Ay + B sin (C z), where A., B and C are constants.
Which of the following have same dimension?
Which of the following have same dimension?
- a)x and Ay
- b)x and B
- c)C and z-1
- d)All of the above
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Physical quantity x depends on quantities y and z as x = Ay + B sin (C...
Explanation:
Given, x = Ay B sin (C z)
We need to find out which of the following have the same dimension.
a) x and Ay
The dimension of x is [x] = [A] [B]. The dimension of Ay is [Ay] = [A] [y]. Since the dimension of y is L, we get [Ay] = [A] L.
Therefore, [x] ≠ [Ay] as the dimension of [B] is not accounted for in [Ay].
b) x and B
The dimension of x is [x] = [A] [B]. The dimension of B is [B] = 1. Therefore, [x] ≠ [B].
c) C and z-1
The dimension of C is [C] = T^-1. The dimension of z-1 is [z-1] = L^-1. Therefore, [C] ≠ [z-1].
d) All of the above
None of the above options have the same dimension.
Hence, the correct answer is option 'D'.
Given, x = Ay B sin (C z)
We need to find out which of the following have the same dimension.
a) x and Ay
The dimension of x is [x] = [A] [B]. The dimension of Ay is [Ay] = [A] [y]. Since the dimension of y is L, we get [Ay] = [A] L.
Therefore, [x] ≠ [Ay] as the dimension of [B] is not accounted for in [Ay].
b) x and B
The dimension of x is [x] = [A] [B]. The dimension of B is [B] = 1. Therefore, [x] ≠ [B].
c) C and z-1
The dimension of C is [C] = T^-1. The dimension of z-1 is [z-1] = L^-1. Therefore, [C] ≠ [z-1].
d) All of the above
None of the above options have the same dimension.
Hence, the correct answer is option 'D'.
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Community Answer
Physical quantity x depends on quantities y and z as x = Ay + B sin (C...
• Since addition is being used x, Ay and B sin(Cz) must have same units.
• The quantity inside sin must have no dimensions so,
[C][z] = 1
=> C and (1/z) have same units
• sin of any number always gives a number. So, B sin(Cz) and B have same units equal to that of Ay and x.
So all the statements are correct
• The quantity inside sin must have no dimensions so,
[C][z] = 1
=> C and (1/z) have same units
• sin of any number always gives a number. So, B sin(Cz) and B have same units equal to that of Ay and x.
So all the statements are correct
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Physical quantity x depends on quantities y and z as x = Ay + B sin (C z), where A., B and C are constants.Which of the following have same dimension?a)x and Ayb)x and Bc)C and z-1d)All of the aboveCorrect answer is option 'D'. Can you explain this answer?
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