Question

The rate of mass of the gas emitted from rear of gas
a rocket is initially 20 kg/s. If the speed of the
relative to the rocket is 800 m/s and mass of
rocket is 1000 kg, then the initial acceleration of
the rocket is (Take g = 10 m/s2)
(1) 4 m/s2
(2) 16 m/s2
(3) 6 m/s2
(4) 12 m/s2 ​

Answer 1

Answer:  6 m/s2

Explanation:

Answer 2

Answer:

• Initial acceleration of rocket = 16 m/s²

OPTION (2) is correct.

Explanation:

Given,

• Rate of mass of gas emited, d(m)/d(t) = 20 kg/s
• Speed of gas relative to rocket, v = 800 m/s
• Mass of rocket, M = 1000 kg

To find,

• The initial acceleration of the rocket, a =?

Knowledge required,

• For a motion of System of Particles, The total external force (F) is equal to the rate of change of the total linear momentum (p) of the system.

       F = d (p) / d (t)

[ F is force, p is momentum, t is time ]

Solution,

In the given condition,

the upthrust force acting on the rocket will be,

→ F = mass of rocket × acceleration of the rocket

→ F = M × a

→ F = 1000 × a

→ F = 1000 a  Newton    _____equation (1)

Also,

→ F = d (p) / d (t)

→ F = d ( m v ) / d ( t )

In the given condition the velocity is constant, but emitting mass of gas is variable, so

→ F = v · [d (m) / d (t)]

→ F = ( 800 ) · ( 20 )

→ F = 16000 Newton   ______equation (2)

By equation (1) and (2)

→ 1000 a = 16000

→ a = 16  m/s²

Therefore,

• The Initial acceleration of the rocket would be 16 m/s².