Question

A helicopter of mass $2000kg$ rises with a vertical acceleration of $15m$ $s^{-2}.$ The total mass of the crew and passengers is $500kg$. Choose the correct statements from the following. (Take$g=10m{s}^{-2}$)
(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.

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

Answer 1

Answer: (D)

Here, Mass of helicopter, $M=2000kg$
Mass of the crew and passengers, $m=500kg$
Vertically upwards acceleration, $a=15m$ $s^{-2}$ $g=10m$ $s^{-2}$
(i) Force on the floor by the crew and passengers
$=m\left(g+a\right)$ $=500kg$ $\left(10+15\right)m$ $s^{-2}$
$=12500N$ $=1.25\times 10^{4}N$
It acts vertically downwards.
(ii) Action of the rotor of the helicopter on the surrounding air $=\left(M+m\right)$ $\left(g+a\right)$
$=\left(2000+500\right)kg$ $\left(10+15\right)m$ $s^{-2}$
$=62500N$ $=6.25\times 10^{4}N$
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.