Find the mass of the rocket as a function of time, 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 its mass initially was `m_0`.

Answer

A

Explanation

`F/m=(v_r(-(dm)/(dt)))/(m)=a=const ant`
`:. (u(-(dm)/(dt)))/(m)=a`
`:. underset(m_0)overset(m)int-(dm)/(m)=underset(0)overset(t)inta/udt`
Solving this equation we get,
`m=m_0e^(-at//u)`