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 :

[Use g = 10 m/s² ]

(1) 6.0 × 10² kg s^–1

(2) 500 kg s^–1

(3) 10 kg s^–1

(4) 60 kg s^–1

Answer 1

Correct Option is (4) 60 kg s^–1

Answer 2

mass of rocket             :   m=1000 kg

acceleration of rocket  :   a=20 ms^-2                      

speed of gases come out with respect to rocket                                         : v=500ms^-1

                    F = mg

                   dp/dt=mg

           

                    d(mv)/dt=mg

        

                   mdv/dt + vdm/dt =mg

                   m a + v dm/dt =mg

 

                   1000 X 20 + 500  dm/dt =1000X(-10)

              500dm/dt = -20000-10000

               500dm/dt = -30000

           

                       dm/dt =- 30000/500

 

                         dm/dt =-60kg s^-1