1.

A rocket of initial mass m_(0) moving with a velocity of upsilon discharges a jet of gases of mean density rho and effective area A. The minimum value of v of fuel gas which enables the rocket to rise vertically above is nearly :

Answer»

`((rhog)/(m_(0)A))^(1//2)`
`((rhog)/(m_(0)))^(1//2)`
`((m_(0)G)/(rhoA))^(1//2)`
`((2m_(0)gA)/(rho))^(1//2)`

Solution :Here `(dm)/(dt) = Aupsilon`
`:.F=(dm)/(dt)upsilonrho.upsilon=A.upsilon.rho`
LEAST force REQUIRED `= m_(0)g`
`:. m_(0)g = A.upsilon^(2)rho`
or `upsilon^(2)=(m_(0)g)/(Arho)`or`upsilon=((m_(0)g)/(A rho))^(1)/(2)`
(c) is the choice


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