The expression given below shows the variation of velocity (v) with time (t), . The dimension of ABC is : [2025]

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Solution

Q.
The expression given below shows the variation of velocity (v) with time (t), $v = A t^{2} + \frac{B t}{C + t}$ . The dimension of ABC is : [2025]

1 $[M^{0} L^{2} T^{- 3}]$

2 $[M^{0} L^{1} T^{- 3}]$

3 $[M^{0} L^{1} T^{- 2}]$

4 $[M^{0} L^{2} T^{- 2}]$

Ans.
(1)

$v = A t^{2} + \frac{B t}{C + t}$

$[v] = [A] t^{2} = [\frac{B t}{C + t}]$

[A] = $L T^{- 3}$

[C] = T

[B] = $L T^{- 1}$

[ABC] = $L^{2} T^{- 3}$

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