37.CAREER INSTITUTERAJASTAA rocket of mass 120 kg. is fired in a gravi

1.	37.CAREER INSTITUTERAJASTAA rocket of mass 120 kg. is fired in a gravity freespace is ejecting gases with velocity 600 m/s atthe rate of 1 kg/s. What will be the initialacceleration of the rocket?(1) 1 m/s2(2) 5 m/s2(3) 10 m/s2O(4) 15 m/s2
Answer» Here, M = 120 kg u = 600 m/s dm/dt = -1 kg/s negative because mass is decreasing with time From Rocket propulsion analysis we have mdv = -udm => dv/dm = -u/m ---1. We know from Momentum equation Let m be the mass of the rocket at an instant and v its velocity at instant F = d/dt(mv) = v(dm/dt) + m(dv/dt) Using chain rule dv/dt = (dv/dm)(dm/dt) F = v(dm/dt) + m(dv/dm)(dm/dt) Using eqn. 1 = v(dm/dt) + m(-u/m)(dm/dt) = v(1) – u(-1) = v + u At the beginning velocity of the rocket was 0, v = 0 F = u = 600 So initial thrust = 600 N Initial acceleration = 600/120 = 5 ms-2 option 2 is the best or correct answer

37.CAREER INSTITUTERAJASTAA rocket of mass 120 kg. is fired in a gravity freespace is ejecting gases with velocity 600 m/s atthe rate of 1 kg/s. What will be the initialacceleration of the rocket?(1) 1 m/s2(2) 5 m/s2(3) 10 m/s2O(4) 15 m/s2

Answer»

Here,

M = 120 kg

u = 600 m/s

dm/dt = -1 kg/s

negative because mass is decreasing with time

From Rocket propulsion analysis we have

mdv = -udm

=> dv/dm = -u/m ---1.

We know from Momentum equation

Let m be the mass of the rocket at an instant and v its velocity at instant

F = d/dt(mv)

= v(dm/dt) + m(dv/dt)

Using chain rule

dv/dt = (dv/dm)(dm/dt)

F = v(dm/dt) + m(dv/dm)(dm/dt)

Using eqn. 1

= v(dm/dt) + m(-u/m)(dm/dt)

= v(1) – u(-1)

= v + u

At the beginning velocity of the rocket was 0,

v = 0

F = u = 600

So initial thrust = 600 N

Initial acceleration = 600/120 = 5 ms-2

option 2 is the best or correct answer

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