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Question

A helicopter of mass 2000 kg rises with a vertical acceleration of 15 ms2. The total mass of the crew and passengers is 500 kg. Choose the correct statement from the following. (Take g=10ms1)
(i) The force on the floor of the helicopter by the crew and passengers is 1.25×104N vertically downwards.
(ii) The action of the rotor of the helicopter on the surrounding air is 6.25×104 vertically downwards.
(iii) The force the helicopter due to the surrounding air is 6.25×104N vertically upwards.

A
(i) and (ii)
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B
(ii) and (iii)
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C
(i) and (iii)
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D
All the three
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Solution

The correct option is D All the three
Here,
Mass of the helicopter, M=2000Kg
Mass of the crew and passengers, m=500kg
Vertically upwards acceleration, a= 15 ms2
g=10ms2

(i) Force on the floor by the crew and passengers
=m(g+a)=500kg(10+15)ms2
=12500N=1.25×104N
It acts vertically downwards.

(ii) The action of the rotor of the helicopter on the surrounding air=(M+m)(g+a)
=(2000+500)kg(10+15)ms2
=62500N=6.25×104N
It acts vertically downwards.

(iii) Force on the helicopter due to the surrounding air is equal and opposite to the action of the rotor of the helicopter on the surrounding air.
Force on the helicopter due to the surrounding air =6.25×104N
It acts vertically upwards.

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