If `v = alpha sin (betat)` where v is meter per second and t is in second then. Find sum of dimesions with respect to the time of `alpha` and `beta`

Question

If `v = alpha sin (betat)` where v is meter per second and t is in second then. Find sum of dimesions with respect to the time of `alpha` and `beta`

If `v = alpha sin (betat)` where v is meter per second and t is in second then. Find sum of dimesions with respect to the time of `alpha` and `beta`
A. 1
B. `-1`
C. 2
D. `-2`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - D
`v = alpha sin (beta t)`
By dimensional homogenity `alpha` has same dimension of `v = [LT^(-1)] sin (betat)` and `sin (beta t)` no dimension as it is trgonometric function
`alpha = M^(0)L^(1)T^(-1)`
`beta = M^(0)L^(0)T^(-1)`
so w.r.t. = dimensions are `(-1) + (-1) = -2`

4 views Answered 2023-02-05 15:29