Question

Find the dimension of :
1. Velocity
2. Power
3. Pressure
4. Volume
5. Potential Energy​

Answer 1

Explanation:

1.velocity is dimensionally represented as [M0 L1 T-1].

2 P = [M1 L2 T-2] × [T-1] = M1 L2 T-3. Therefore, power is dimensionally represented as M1 L2 T-3.

3.M1 L1 T-2] × [L2]-1 = M1 L-1 T -2. Therefore, the pressure is dimensionally represented as M1 L-1

Answer 2

Answer:

Velocity:

$\longrightarrow\sf velocity = \dfrac{Displacement}{Time}$

$\longrightarrow\sf [v]= \dfrac{[x]}{[t]}$

$\longrightarrow\sf [v]= \dfrac{[L]}{[T]}$

$\longrightarrow\sf [v]= [L][T^{ - 1} ]$

$\longrightarrow\bf [v]= [M^0L^1T^{ - 1} ]$

Power :

$\longrightarrow\sf Power = Force \times velocity$

$\longrightarrow\sf [P] = [F] [v]$

$\longrightarrow\sf [P] = [M^1L^1T^{-2}] [L^{1} T^{-1}]$

$\longrightarrow\bf [P] = [M^1L^2T^{-3}]$

Pressure:

$\longrightarrow\sf Pressure = \dfrac{Force}{Area}$

$\longrightarrow\sf [P] = \dfrac{[F]}{[A]}$

$\longrightarrow\sf [P] = \dfrac{[M^1L^1T^{-2}]}{[L^2]}$

$\longrightarrow\sf [P] = [M^1L^1T^{-2}][L^{ - 2}]$

$\longrightarrow\bf [P] = [M^1L^{ - 1} T^{-2}]$

Volume:

$\longrightarrow\sf Volume = Length \times Breadth \times Height$

$\longrightarrow\sf [V] =[L][L][L]$

$\longrightarrow\bf [V] =[L ^{3} ]$

Potential energy:

$\longrightarrow\sf Potential \: energy = mass \times acceleration \: due \: to \: gravity \times Height$

$\longrightarrow\sf [U]=[m][g][H]$

$\longrightarrow\sf [U]=[M][LT^{-2}][L]$

$\longrightarrow\bf [U]=[M^{1} L^{2} T^{-2}]$