Question 44: Units , Dimensions and Error Analysis

Question

The expression given below shows the variation of velocity (
v
) with time (
t
),
$v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}$.
The dimension of ABC is :

Accepted Answer

$$\begin{aligned}
& {\left[\mathrm{LT}^{-1}ight]=[\mathrm{A}]\left[\mathrm{T}^2ight]=\frac{[\mathrm{B}][\mathrm{T}]}{[\mathrm{C}]+[\mathrm{T}]}} \
& {[\mathrm{C}]=[\mathrm{T}]} \
& {[\mathrm{A}]=\left[\mathrm{LT}^{-3}ight]} \
& {[\mathrm{B}]=\left[\mathrm{LT}^{-1}ight]} \
& {[\mathrm{ABC}]=\left[\mathrm{L}^2 \mathrm{~T}^{-3}ight]}
\end{aligned}$$

Answer

[M
0
L
1
T
−2
]

Answer

[M
0
L
2
T
−3
]

Answer

[M
0
L
2
T
−2
]

Answer

[M
0
L
1
T
−3
]

Units , Dimensions and Error Analysis

The expression given below shows the variation of velocity ( v ) with time ( t ), v=\mathrm{At}^2+\frac{\mathrm{Bt}}{\mathrm{C}+\mathrm{t}}. The dimension of ABC is :

Choose the correct answer: