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Ncert): A Man Walking Briskly In Rain With Speed V Must Slant His Umbrella Forward Making An Angle θ With The Vertical. A Student Derives The Following Relation Between θ And V : Tan θ = V And Checks That The Relation Has A Correct Limit: As V → 0, θ →0, As Expected. (we Are Assuming There Is No Strong Wind And That The Rain Falls Vertically For A Stationary Man). Do You Think This Relation Can Be Correct ? If Not, Guess The Correct Relation? |
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Answer» Given, V = tanθ Dimensions of LHS = [v] = [M0L1T-1] Dimension of RHS = [tanθ] = [M0L0T0] (trigonometric ratios are dimensionless) Since [LHS] ≠ [RHS]. Equation is dimensionally INCORRECT. To MAKE the equation dimensionally correct, LHS should also be dimension less. It may be possible if consider speed of rainfall (Vr) and the equation will become: TAN θ = v/Vr Given, v = tanθ Dimensions of LHS = [v] = [M0L1T-1] Dimension of RHS = [tanθ] = [M0L0T0] (trigonometric ratios are dimensionless) Since [LHS] ≠ [RHS]. Equation is dimensionally incorrect. To make the equation dimensionally correct, LHS should also be dimension less. It may be possible if consider speed of rainfall (Vr) and the equation will become: tan θ = v/Vr |
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