If is given that B= Rate of burn of fuel mass
So can we right B=dm/dt or -dm/dt, which of these is accurate?
if m is the mass of the rocket, the -dm/dt is more useful.
Here, m is the mass of the fuel remaining
Mass of system=massofrocket + massoffuel
dMassofSystem/dt=dm/dt and it is negataive. I assume the mass of the rocket does not change.
To determine whether B should be written as dm/dt or -dm/dt, we need to consider the context and the sign convention being used.
In this case, B represents the rate of burn of fuel mass. To determine the correct sign convention, we need to define what positive and negative values of B indicate in this context.
If positive values of B indicate an increase in burn rate (i.e., fuel mass is being burned), and negative values indicate a decrease in burn rate (i.e., fuel mass is being added), then we should write B as dm/dt.
On the other hand, if positive values of B indicate a decrease in burn rate (i.e., fuel mass is being consumed), and negative values indicate an increase in burn rate (i.e., fuel mass is being added), then we should write B as -dm/dt.
Without further information about the specific context and sign convention being used, it is not possible to determine whether B should be expressed as dm/dt or -dm/dt. It is important to clarify the sign convention being used in the given problem or equation in order to make an accurate representation of B.