Question

A $$5000\,kg$$   rocket is set for vertical firing. The exhaust speed is $$800\,m{s^{ - 1}}.$$   To give an initial upward acceleration of $$20\,m{s^{ - 2}},$$   the amount of gas ejected per second to supply the needed thrust will be
$$\left( {g = 10\,m{s^{ - 2}}} \right)$$

A. $$127.5\,kg\,{s^{ - 1}}$$
B. $$187.5\,kg\,{s^{ - 1}}$$  
C. $$185.5\,kg\,{s^{ - 1}}$$
D. $$137.5\,kg\,{s^{ - 1}}$$
Answer :   $$187.5\,kg\,{s^{ - 1}}$$
Solution :
Given: Mass of rocket $$\left( m \right) = 5000\,kg$$
Exhaust speed $$\left( v \right) = 800\,m/s$$
Acceleration of rocket $$\left( a \right) = 20\,m/{s^2}$$
Gravitational acceleration $$\left( g \right) = 10\,m/{s^2}$$
We know that upward force
$$F = m\left( {g + a} \right) = 5000\left( {10 + 20} \right) = 5000 \times 30 = 150000\,N.$$
We also know that amount of gas ejected
$$\left( {\frac{{dm}}{{dt}}} \right) = \frac{F}{v} = \frac{{150000}}{{800}} = 187.5\,kg/{s^{ - 1}}$$

Releted MCQ Question on
Basic Physics >> Impulse

Releted Question 1

The figure shows the position-time $$\left( {x - t} \right)$$  graph of one dimensional motion of a body of mass $$0.4kg.$$  The magnitude of each impulse is
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A. $$0.4Ns$$
B. $$0.8Ns$$
C. $$1.6Ns$$
D. $$0.2Ns$$
Releted Question 2

A rigid ball of mass $$m$$ strikes a rigid wall at $${60^ \circ }$$ and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be
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A. $$mv$$
B. $$2mv$$
C. $$\frac{{mv}}{2}$$
D. $$\frac{{mv}}{3}$$
Releted Question 3

The force $$F$$ acting on a particle of mass $$m$$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from $$0$$ to $$8 s$$  is
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A. $$24\,N{\text{-}}s$$
B. $$20\,N{\text{-}}s$$
C. $$12\,N{\text{-}}s$$
D. $$6\,N{\text{-}}s$$
Releted Question 4

A man of $$50\,kg$$  mass is standing in a gravity free space at a height of $$10\,m$$  above the floor. He throws a stone of $$0.5\,kg$$  mass downwards with a speed $$2\,m{s^{ - 1}}.$$  When the stone reaches the floor, the distance of the man above the floor will be

A. $$9.9\,m$$
B. $$10.1\,m$$
C. $$10\,m$$
D. $$20\,m$$

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