Question

In case of a variable mass system, a thrust force of magnitude $\left|V_r\frac{dm}{dt}\right|$ has to be applied on the system, whose mass is changing. Which of the following statements is/are correct?

• A. Direction of thrust force is along $V_r$ if the mass is increasing.
• B. Direction of thrust force is opposite to $V_r$ if the mass is increasing
• C. Direction of thrust force is opposite to $V_r$ if the mass is decreasing.
• D. Direction of thrust force is along $V_r$ if the mass is decreasing.

Answer 1

Answer: (A), (C)

Direction of thrust force is opposite to $V_r$ if the mass is decreasing.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> If mass is decreasing, $F=-V_r\frac{dm}{dt}$
$\Rightarrow F$ and $V_r$ are in opposite directions.
If mass is increasing, $F=V_r\frac{dm}{dt}$
$\Rightarrow F$ and $V_r$ are along the same direction.