Write the dimensions of a and b in the relation: P=b−x2at Where P is power, x is distance and t is time.
[M0L2T0],[M−1L0T2]
[M0L2T0],[M−1L1T2]
[M−1L1T2],[M0L2T0]
[M−1L0T2],[M0L2T0]
A
[M0L2T0],[M−1L0T2]
B
[M−1L0T2],[M0L2T0]
C
[M0L2T0],[M−1L1T2]
D
[M−1L1T2],[M0L2T0]
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Solution
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Dimensions of Power: P−ML2T−3
Since the given expression is dimensionally correct, each term of the expression must have same dimensions as that of power.
Therefore,[x2][a][t]=L2[a]T=ML2T−3
⇒[a]−M−1L0T2
[b][a][t]=[b](M−1L0T2)(T)=ML2T−3
⇒[b]−L2
Hence, Option A is correct.
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