find the effective weight of an astronuat ordinarily weighing 50kg when his rocket moves vertically upwards with 6gm acceleration
What do you mean by 6 "gm" acceleration? Grams are not used to measure acceleration. Do you mean 6 g? Or 6 m/s^2
In either case, the effective weight is F = m a
where a is the acceleration rate of the rocket. If the astronaut is close to Earth, a gravitational weight term must be added.