Question

Á rocket of mass 800 kg is to be projected vertically
upwards. The gases are exhausted vertically
downwards with velocity 40 m/s with respect to the
rocket. What is the minimum rate of burning fuel, so
as to just lift the rocket upwards against the
gravitational attraction ? (Take g = 10 m/s)
(1) 80 kg/s
(2) 400 kg/s
(3) 200 kg/s
(4) 800 kg/s
​

Answer 1

Answer

• Option 3 is correct
• Minimum rate of burning fuel = 200 kg/s

Given

Á rocket of mass 800 kg is to be projected vertically  upwards. The gases are exhausted vertically  downwards with velocity 40 m/s with respect to the  rocket

To Find

Minimum rate of burning fuel

Solution

From attachment ,

$\rm Upward\ force\ exerted=Weight\ of\ rocket\\\\\implies \rm Rate\ of\ burning\ fuel\ \times Velocity=Mass\ \times g\\\\\implies \rm M\ \times v=m\ \times g\\\\\implies \rm M\ \times 40=800\ \times 10\\\\\implies \rm M=\dfrac{800\ \times 10}{40}\\\\\implies \rm M=20\ \times 10\\\\\implies \rm M=200\ Kg/s$

So , Minimum rate of burning fuel is 200 Kg/s

Answer 2

◘ Given ◘

$\bigstar$ A rocket of mass 800 kg is to be projected vertically  upwards.

$\bigstar$ The gases are exhausted vertically  downwards with velocity 40 m/s with respect to the  rocket.

$\bigstar$ Acceleration due to gravity, g = 10 m/s²

◘ To Find ◘

The minimum rate of burning fuel, so  as to just lift the rocket upwards against the  gravitational attraction.

◘ Solution ◘

The upward force faced by the rocket = Weight of the rocket

_________________

→ Weight of the rocket, W = Mass × g

→ W = 800 × 10

→ W = 8000 N

_________________

⇒ Rate of burning fuel × Velocity of gases exhausted vertically  downwards = 8000

⇒ R × 40 = 8000

⇒ R = 8000/40

⇒ R = 800/4

⇒ R = 200 kg/s

Therefore, the minimum rate of burning fuel, so  as to just lift the rocket upwards against the  gravitational attraction is 200 kg/s.