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

Rocket Mechanism

Find the mass...

Question

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 $m_{0}$ .

m = m_{0} e^{- a t / u}

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

m = m_{0} e^{- t / u}

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

m = m_{0} e^{a t / u}

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

m = m_{0} e^{2 a t / u}

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

Open in App

Solution

The correct option is A $m = m_{0} e^{- a t / u}$

Since $F_{e x t} = 0$ , we get
$F_{n e t} = V_{r} (\frac{- d m}{d t}) = u \frac{- d m}{d t}$ ... (I)
Also $F_{n e t} = m a$ ...(II)

By eq. (I) and (II)
$m a = - u \cdot \frac{d m}{d t}$
Integrating,
$\int_{m_{0}}^{m} \frac{d m}{m} = \int_{0}^{t} \frac{- a d t}{u}$
$\Rightarrow [ln \frac{m}{m_{0}}] = \frac{- a t}{u}$
$\Rightarrow \frac{m}{m_{0}} = e^{- a t / u}$
$\Rightarrow m = m_{0} e^{- a t / u}$

Suggest Corrections

Similar questions

t

a

u

m_{0}

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

w

u

m_{0}

a

u

m_{0}

m

m^{'}

m_{0}

u_{r e l}

v =

m_{0}

_{0}

u

m

α = \frac{u}{v_{0}} ln (\frac{x m_{0}}{m})

x

Join BYJU'S Learning Program