Question

A rocket is gong upwards with accelerated
motion. A man sitting in it feels his weight
increased 5 times his own weight. If the mass
of the rocket including that of the man is
1.0x104kg, how much force is being applied by
rocket engine? (Take g = 10 ms 2)
5x104N
5x10ʻN
5x10'N
(0 O
2x10*N​

Answer 1

Given:

Total mass(man+rocket), m` =1.0×10⁴ kg

Now:

The mass of man sitting in the rocket is increased by 5 times.

As force due to mass = mg,

$\tt\pink{So, a = 5g = 5 × 10 = 50m/s²}$

.

Force applied by the rocket engine,

$\tt\red{F=ma=1.0×10⁴ ×50=5×10^5 N}$

Answer 2

F.B.D:-

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As the man is sitting inside an accelerated rocket (non - inertial frame of reference), a pseudo force equal to $\sf ma$ will be acting on him, in the downward direction. This force will responsible for increasing his apparent weight.

True Weight:-

$\quad\quad\bullet \sf True\: Weight\: =\: mg\quad\quad\dots (1)$

Apparent Weight:-

$\sf ma + mg$

$\longrightarrow \sf m(a + g)\quad\quad\dots(2)$

According to the question, the difference between apparent weight and true weight is 5 times the true weight

$\small \sf Apparent \:weight\:-\: True\: weight = 5(True \:Weight)$

$\longrightarrow \small \sf m(a + g) - mg = 5mg\quad[From\:(1)\:and\:(2)]$

$\longrightarrow \sf ma + mg - mg = 5mg$

$\longrightarrow \sf ma = 5mg$

$\longrightarrow \sf a = 5g$

$\longrightarrow \sf a = 50 \:m/s^2\quad\quad\dots(3)$

Let the total mass (Mass of man + Mass of rocket) be $\sf M = 1 \times 10^4 \: kg \quad\quad\dots(4)$

$\longrightarrow \sf F_{(engine)} = M \times a$

$\longrightarrow \small \sf F_{(engine)} = 1 \times 10^4 \times 50 \quad[From\:(3)\:and\:(4)]$

$\longrightarrow \sf \underline{\underline{\sf{\green{F_{(engine)} = 5 \times 10^5\:N }}}}$