A helicopter of mass 2000 kg rises with a vertical acceleration of 15 . The total mass of the crew and passengers is 500 kg. Choose the correct statements from the following.

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 statements from the following. (Take g = 10 $m s^{- 2}$ )

(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 $6.25 \times 10^{4} N$ vertically downwards.

(iii) The force on the helicopter due to the surrounding air is $6.25 \times 10^{4} N$ vertically upwards.

Smart Achievers · Accepted Answer

(4)

Here, Mass of helicopter, $M = 2000 kg$

Mass of the crew and passengers, $m = 500 kg$

Vertically upwards acceleration, $a = 15 {m s}^{- 2}$ , $g = 10 {m s}^{- 2}$

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

$= m (g + a)$ $= 500 kg (10 + 15) {m s}^{- 2} = 12500 N = 1.25 \times 10^{4} N$

It acts vertically downwards.

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

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

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.

$∴$ Force on the helicopter due to the surrounding air $= 6.25 \times 10^{4}$ N

It acts vertically upwards.

Solution

1 (i) and (ii)

2 (ii) and (iii)

3 (i) and (iii)

4 All the three

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