CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

COM in Collision and Explosion

A rocket is m...

Question

A rocket is moving up with constant acceleration $a$ . Assume external force on it to be zero. Exhaust gases escape with velocity $u$ relative to the rocket. Find how its mass changes with time if its initial mass is $m_{0}$

Open in App

Solution

Since external force is zero which means rocket gets propelled by relative change of momentum of exhaust with respect to rocket. Hence net force = rate of change of momentum of exhaust= $- d m / d t \times u = m a$ Integrating this and putting limits $m_{i} = m_{0}$ and $m_{f} = m$ we get $m = m_{0} e^{- a / u}$ .

Suggest Corrections

thumbs-up

0

Similar questions

Q. Find the mass

(m)

of the rocket as a function of time, if it moves with a constant acceleration

a

in the absence of external force. The gas escapes with a constant velocity

u

relative to the rocket and its initial mass was

m_{0}

.

Q. What will be the mass of the rocket at a certain instant of time

t

, if it moves with a constant acceleration

a

, in absence of external forces?

The gas escapes with a constant velocity

u

relative to the rocket, and initial total mass of the rocket was

m_{0}

.

Q. If the relation between the mass of the rocket and time is given as

m = m_{0} e^{- (\frac{x w t}{u})}

, when the rocket moves with a constant acceleration

w

, the external forces are absent, the gas escapes with a constant velocity

u

relative to the rocket, and its mass at the initial moment equals

m_{0}

Q. A rocket motor consumes

100 K g

of fuel per second, exhausting it with a speed of

5 \times 10^{3} m s^{- 1}

. (i) What force is exerted on the rocket? (ii) What will be the velocity of the rocket at the instant its mass is reduced (

1 / 20

)th of its initial mass, its initial velocity being zero. Neglect gravity.

Q. A rocket of initial mass

6000 k g

eject gases at a constant rate of

16 k g s^{- 1}

with constant relative speed of

11 k m s^{- 1}

. What is the acceleration of rocket one minute after the blast?

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Why Is the Center of Mass the Real Boss?

PHYSICS

Watch in App

explore_more_icon

Explore more

COM in Collision and Explosion

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon