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2 years ago

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A student has derived the following nondimensionally homogeneous equation:a=xt2−vt+Fmwhere v is a velocity's magnitude, a is an

acceleration's magnitude, t is a time, m is a mass, F is a force's magnitude, and x is a distance (or length). Which terms are dimensionally homogeneous?

1 answer:

ahrayia [7]2 years ago

6 0

Answer:

None of the terms are dimensionally homogeneous

Explanation:

$a=xt^{2}-vt+Fm$

dimensions from each term:

$a:\frac{L}{T^{2}}$

$xt^{2}:L*T^{2}$

$vt:\frac{L}{T}*T=L$

$Fm:N*Kg=\frac{M*L}{T^{2}}*M=\frac{M^{2}*L}{T^{2}}$

we observe that there are no terms with equal dimensions, that is to say none of the terms are dimensionally homogeneous

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When two resistors are wired in series with a 12 V battery, the current through the battery is 0.33 A. When they are wired in pa

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Answer:

If R₂=25.78 ohm, then R₁=10.58 ohm

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Explanation:

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V = Voltage of battery = 12 V

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I = Current = 1.6 A (parallel)

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In parallel

$\text{Equivalent resistance}=\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}\\\Rightarrow {R_{eq}=\frac{R_1R_2}{R_1+R_2}$

$\text {From Ohm's law}\\V=IR_{eq}\\\Rightarrow R_{eq}=\frac{12}{1.6}\\\Rightarrow \frac{R_1R_2}{R_1+R_2}=7.5\\\Rightarrow \frac{R_1R_2}{36.36}=7.5\\\Rightarrow R_1R_2=272.72\\\Rightarrow(36.36-R_2)R_2=272.72\\\Rightarrow R_2^2-36.36R_2+272.72=0$

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∴ If R₂=25.78 ohm, then R₁=10.58 ohm

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Explanation:

Given that,

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1 year ago

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Answer:

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