The relation between displacement (X) of a particle and time (t) is given by the following equation: X = At + Bt². What will be the dimensions of A/B, if the equation is dimensionally correct?
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A.
[T]
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B.
[T3]
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C.
[T−3]
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D.
[T−1]
Correct Answer:
A. [T]
Explanation:
According to the principle of dimensional homogeneity, each term in a physical equation must have the same dimensions. In the given equation, displacement X has the dimension of length [L], and time t has the dimension of time [T]. Therefore, both At and Bt2 must also have the dimension of [L].
For the first term:
At = \[L\]
A\[T\] = \[L\]
A = \[L\]\[T-1\]
For the second term:
Bt2 = \[L\]
B\[T\]2 = \[L\]
B = \[L\]\[T-2\]
To find the dimensions of A/B:
A/B = \[L\]\[T-1\] / \[L\]\[T-2\]
A/B = \[T-1\] / \[T-2\]
A/B = \[T\]
The resulting dimension is [T], which matches the first option provided in the spreadsheet.
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