Question

A helicopter of mass 2000 kg rises with a vertical acceleration of 15 $m{s}^{-2}$. The total mass of the crew and passengers is 500 kg. Choose the correct statement from the following. (Take g=10$m{s}^{-1}$)
(i) The force on the floor of the helicopter by the crew and passengers is $1.25\times {10}^{4}N$ vertically downwards.
(ii) The action of the rotor of the helicopter on the surrounding air is $6.25\times {10}^4$ vertically downwards.
(iii) The force the helicopter due to the surrounding air is $6.25\times {10}^{4}N$ vertically upwards.

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

Answer 1

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 $m{s}^{-2}$
g=10$m{s}^{-2}$

(i) Force on the floor by the crew and passengers
$=m(g+a)=500kg(10+15)$$m{s}^{-2}$
$=12500N=1.25\times {10}^{4}N$
It acts vertically downwards.

(ii) The action of the rotor of the helicopter on the surrounding air$=(M+m)(g+a)$
$=(2000+500)kg(10+15)m{s}^{-2}$
$=62500N=6.25\times {10}^{4}N$
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.
$\therefore$ Force on the helicopter due to the surrounding air =$6.25\times {10}^{4}N$
It acts vertically upwards.