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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) `[intvdt]=[vt]=[LT^(-1)xxT]=[M^(0) L^(1) T^(0)]` (iv) `[int adt]=[at]=[LT^(-2)xxT]=[M^(0) L^(1) T^(-1)]`
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