Find the velocity $v$ of the rocket at the moment when its mass is equal to $m$ , if at the initial moment it possessed the mass $m_{0}$ and its velocity was equal to zero.

\to v = - \to u ln \frac{m}{m_{0}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\to v = \to u ln \frac{m}{m_{0}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\to v = \to u ln \frac{m_{0}}{m}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\to v = - \to u ln \frac{m_{0}}{m}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\to v = - \to u ln \frac{m_{0}}{m}$
Decrease in mass of rocket is responsible for increase in its velocity
Net Force $= m a = u \frac{d m}{d t} \Rightarrow m \frac{d v}{d t} = u \frac{d m}{d t}$
$∴ \int_{0}^{v} d v = u \int_{m_{o}}^{m} \frac{d m}{m} \Rightarrow v = u l n (\frac{m}{m_{o}})$
$∴ v = - u l n (\frac{m_{o}}{m})$

Suggest Corrections

Similar questions

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. 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}

A freight car is moving on smooth horizontal track without any external force. Rain is falling at the rate of u m/s at an angle $θ$ with the vertical. Rain drops are collected in the car at the rate of $μ$ kg/s. If initial mass of the car is $m_{0}$ and velocity $v_{0}$ then find its velocity after time it.