The power for hovering helicopter depends on its linear size, the density of air and (g$$×density of the $$helicopter) as p∝ $$($$ linear size $$)x$$ $$($$ density of air $$)y(g$$× density of helicopter $$)z$$ where g is acceleration due to gravity. Find the ratio of power output of engines of two helicopters $$p1p2$$, when linear size of first helicopter is four times the linear size of the second and all other parameters are same.

Question

The power for hovering helicopter depends on its linear size, the density of air and (g$$×density of the $$helicopter) as p∝ $$($$ linear size $$)x$$ $$($$ density of air $$)y(g$$× density of helicopter $$)z$$ where g is acceleration due to gravity. Find the ratio of power output of engines of two helicopters $$p1p2$$, when linear size of first helicopter is four times the linear size of the second and all other parameters are same.

Infinity Learn · Accepted Answer

p∝$$($$ linear size $$)x($$ density of air $$)y(g$$× density of copter $$)zML2T$$−$$3=$$[L]xML−$$3yML$$−$$2T$$−$$2z$$⇒$$1=y+z2=x$$−$$3y$$−$$2z$$,−$$3=$$−$$2z$$⇒$$z=32$$,$$y=$$−$$12$$,$$x=72p$$∝$$($$ linear size $$)7/2$$⇒$$p1p2=L1L27/2=(4)7/2=(2)7=128$$

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