Recall the formula for momentum.

Physics
Recall the formula for momentum.

ScanSolve AI Answer

Answer

[M][L][T]−1\text{[M][L][T]}^{-1}

Here are the dimensions for the given quantities:

a) Momentum Step 1: Recall the formula for momentum. Momentum (pp) is the product of mass (mm) and velocity (vv). p=mvp = mv Step 2: Substitute the dimensions of mass and velocity. The dimension of mass is [M][M]. The dimension of velocity is [L][T]−1[L][T]^{-1} (length per unit time). [p]=[M]×[L][T]−1[p] = [M] \times [L][T]^{-1} The dimension of momentum is [M][L][T]−1\boxed{[M][L][T]^{-1}}.

b) Pressure Step 1: Recall the formula for pressure. Pressure (PP) is force (FF) per unit area (AA). P=FAP = \frac{F}{A} Step 2: Substitute the dimensions of force and area. The dimension of force is [M][L][T]−2[M][L][T]^{-2} (from F=maF=ma, where aa is acceleration [L][T]−2[L][T]^{-2}). The dimension of area is [L]2[L]^2. [P]=[M][L][T]−2[L]2=[M][L]1−2[T]−2[P] = \frac{[M][L][T]^{-2}}{[L]^2} = [M][L]^{1-2}[T]^{-2} The dimension of pressure is [M][L]−1[T]−2\boxed{[M][L]^{-1}[T]^{-2}}.

c) Surface Tension Step 1: Recall the formula for surface tension. Surface tension (γ\gamma) is force (FF) per unit length (LL). γ=FL\gamma = \frac{F}{L} Step 2: Substitute the dimensions of force and length. The dimension of force is [M][L][T]−2[M][L][T]^{-2}. The dimension of length is [L][L]. [γ]=[M][L][T]−2[L]=[M][L]1−1[T]−2[\gamma] = \frac{[M][L][T]^{-2}}{[L]} = [M][L]^{1-1}[T]^{-2} The dimension of surface tension is [M][T]−2\boxed{[M][T]^{-2}}.

d) Power Step 1: Recall the formula for power. Power (PP) is work done (WW) per unit time (tt). P=WtP = \frac{W}{t} Step 2: Substitute the dimensions of work and time. Work is force times distance (W=F⋅dW = F \cdot d). The dimension of force is [M][L][T]−2[M][L][T]^{-2}. The dimension of distance is [L][L]. So, the dimension of work is [W]=[M][L][T]−2×[L]=[M][L]2[T]−2[W] = [M][L][T]^{-2} \times [L] = [M][L]^2[T]^{-2}. The dimension of time is [T][T]. [P]=[M][L]2[T]−2[T]=[M][L]2[T]−2−1[P] = \frac{[M][L]^2[T]^{-2}}{[T]} = [M][L]^2[T]^{-2-1} The dimension of power is [M][L]2[T]−3\boxed{[M][L]^2[T]^{-3}}.

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a) Momentum Step 1: Recall the formula for momentum. Momentum (p) is the product of mass (m) and velocity (v).

Recall the formula for momentum.
Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

ScanSolve AI Answer
Here are the dimensions for the given quantities: a) Momentum Step 1: Recall the formula for momentum. Momentum (p) is the product of mass (m) and velocity (v). p = mv Step 2: Substitute the dimensions of mass and velocity. The dimension of mass is [M]. The dimension of velocity is [L][T]^-1 (length per unit time). [p] = [M] × [L][T]^-1 The dimension of momentum is [M][L][T]^-1. b) Pressure Step 1: Recall the formula for pressure. Pressure (P) is force (F) per unit area (A). P = (F)/(A) Step 2: Substitute the dimensions of force and area. The dimension of force is [M][L][T]^-2 (from F=ma, where a is acceleration [L][T]^-2). The dimension of area is [L]^2. [P] = [M][L][T]^-2[L]^2 = [M][L]^1-2[T]^-2 The dimension of pressure is [M][L]^-1[T]^-2. c) Surface Tension Step 1: Recall the formula for surface tension. Surface tension () is force (F) per unit length (L). = (F)/(L) Step 2: Substitute the dimensions of force and length. The dimension of force is [M][L][T]^-2. The dimension of length is [L]. [] = [M][L][T]^-2[L] = [M][L]^1-1[T]^-2 The dimension of surface tension is [M][T]^-2. d) Power Step 1: Recall the formula for power. Power (P) is work done (W) per unit time (t). P = (W)/(t) Step 2: Substitute the dimensions of work and time. Work is force times distance (W = F · d). The dimension of force is [M][L][T]^-2. The dimension of distance is [L]. So, the dimension of work is [W] = [M][L][T]^-2 × [L] = [M][L]^2[T]^-2. The dimension of time is [T]. [P] = [M][L]^2[T]^-2[T] = [M][L]^2[T]^-2-1 The dimension of power is [M][L]^2[T]^-3. 3 done, 2 left today. You're making progress.