Question

A helicopter of mass 2000 kg rises with a vertical acceleration of $15 \mathrm {~ms} ^ { - 1 }$ 2, The total mass of the crew and passengers is 500 kg. Choose the correct statements form the following. (Take $\mathrm { g } = 10 \mathrm {~ms} ^ { - 2 }$ )

(i) The force on the floor of the helicopter by the crew and passengers is $1.25 \times 10 ^ { 4 } \mathrm {~N}$ 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 on the helicopter due to the surrounding ai is $6.25 \times 10 ^ { 4 } \mathrm {~N}$ vertically upwards

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

Answer 1

Answer: (D)

All the three

Answer 2

Here

Mass of helicopter, $M = 2000 \mathrm {~kg}$

Mass of the crew and passengers, $m = 500 \mathrm {~kg}$

Vertically upwards acceleration , $a = 15 m s ^ { - 2 }$

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

(i) Force on the floor by the crew and passengers

$= m ( g + a ) = 500 \mathrm {~kg} ( 10 + 15 ) \mathrm { ms } ^ { - 2 }$

$= 12500 N = 1025 \times 10 ^ { 4 } N$

It acts vertically downwards

(ii) Action of the rotor of the helicopter on the surrounding air

$= ( M + m ) ( g + a )$ $= ( 2000 + 500 ) \mathrm { kg } ( 10 + 15 ) \mathrm { ms } ^ { - 2 }$ $= 62500 \mathrm {~N} = 6.25 \times 10 ^ { 4 } \mathrm {~N}$

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