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Find dimensional formula: (i) (dx)/(dt...

Find dimensional formula:
(i) `(dx)/(dt)` (ii) `m(d^(2)x)/(dt^(2))` (iii) `int vdt` (iv) `int adt`
where `x rarr` displacement, `t rarr` time, `v rarr` velocity and `a rarr` acceleration

Text Solution

Verified by Experts

(i) `[(dx)/(dt)] = [(x)/(t)] = [(L)/(T)] = [M^(0) L ^(1) T^(-1)]`
(ii) `[m(d^(2)x)/(dt^(2))] = [m(x)/(t^(2))] = [(ML)/(T^(2)) ] = [M^(1)L^(1)T^(-2)]`
(iii) `[int vdt] = [vt] = [LT^(-1) xx T ] = [M^(0) L^(1)T^(0)]`
(iv) `[int adt] = [at] = [ LT^(-2) xx T] = [M^(0) L^(1) T^(-1)]`
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