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STD 11 - 5. work,energy,power and collision — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 5. work,energy,power and collision4 Marks
MCQ
A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed $v$, the electrical power output will be most likely proportional to
  • A
    $v^4$
  • B
    $v^2$
  • C
    $v$
  • ✓
    $v^3$
✓

Answer

Correct option: D.
$v^3$
d
Power $=\mathrm{F} \bullet \mathrm{v}=\mathrm{Fv} F=v\left(\frac{d m}{d t}\right)=v\left\{\frac{d(\rho \times \text {volume})}{d t}\right\}$

$=\rho v\left\{\frac{d(v o l u m e)}{d t}\right\}=\rho v(A v)=\rho A v^{2} \therefore$ Power $P=\rho A v^{3} \quad$ or $P=v^{3}$

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