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Question: A rocket of mass \(1000kg\) is to be projected vertically upwards. The gases are exhausted verticall...

A rocket of mass 1000kg1000kg is to be projected vertically upwards. The gases are exhausted vertically downward with velocity 100ms−1100m{s^{ - 1}} with respect to the rocket. What is the minimum rate of burning of fuel, so as to just lift the rocket upward against the gravitational attraction? (take g=10ms−2)\left( {take\,g = 10m{s^{ - 2}}} \right):
A. 50kgs−150kg{s^{ - 1}}
B. 100kgs−1100kg{s^{ - 1}}
C. 200kgs−1200kg{s^{ - 1}}
D. 400kgs−1400kg{s^{ - 1}}

Explanation

Solution

Hint - To solve this question, firstly we should learn about velocity and force and the concept behind them. Then, with the help of our knowledge and the formulas required, we will find the required values and quantities. And hence, by using this information we can easily approach our answer.

Step-By-Step answer:
Velocity (of an object) is determined by the rate of change of object’s position with respect to a frame of reference and time it is speeding in a particular direction. It is a vector quantity having SI unit is meter per second. It is the rate of the displacement change. The velocity of moving objects can be zero.
Force is an external agent capable of changing the state of rest or motion of a particular body. It has both magnitude and direction. Force can be measured using a spring balance SI unit of force is Newton(N)\left( N \right). It is a physical cause that can change that state of motion or the dimension of an object. There are two types of forces based on their application are Contact Force, Non- contact Force. Example of contact forces- Muscular Force, Mechanical Force.

Given,
The velocity of consume gases with respect to rocket=100ms−1 = 100m{s^{ - 1}}
The minimal force on the rocket to lift it Fmin⁡=mg=1000×10=10000N{F_{\min }} = mg = 1000 \times 10 = 10000N .
Therefore, minimum rate of burning of fuel is given by
dmdt=Fmin⁡v=10000100\dfrac{{dm}}{{dt}} = \dfrac{{{F_{\min }}}}{v} = \dfrac{{10000}}{{100}}
=100kgs−1= 100kg{s^{ - 1}}

Note - The quantity of force is expressed by the vector product of mass and acceleration. The equation of the formula for force is expressed as F=m×aF = m \times a. Force is a physical cause that can change that state of motion or the dimension of an object.
In simple language, Rocket is a chamber enclosing a gas under pressure. Gas is allowed to escape from a small opening present at one end of the chamber which provides a thrust and hence the rocket gets pushed in the other direction.