Question

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms^-2. The gases come out at a relative speed of 500 ms^-1 with respect to the rocket.

विकल्प

• 60 kg s^-1

• 10 kg s^-1

• 6.0 × 10² kg s^-1

• 500 kg s^-1

Answer 1

60 kg s^-1

Explanation:

An illustration of a variable mass system is a rocket. If the gas leaves the rocket at a relative speed of V_g and the rate of mass loss is `(dm)/(dt)`, then

Upthrust = F = `(dm)/(dt).V_g`

using the free body diagram,

F - mg = ma

⇒ `(dm)/(dt).V_g - mg = ma`

`(dm)/(dt) = (m(g + a))/(V_g)`

= `(1000(10 + 20))/500`

`(dm)/(dt) = 2 xx 30 = 60` kg/s