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.
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answer is 128.
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Detailed Solution
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