n a rocket, the mass of the fuel is 90% of the total mass. The rocket is blasted from the launching pad. If the exhaust gases are ejected at a speed of `1000 S^(-1)` what is the maximum speed attained by the rocket? (Neglect the effects of gravity and air resistance).

Options

A. `2.3 km//s`
B. `1 km//s`
C. `1.5 km//s`
D. `9 km//s`

Answer

a

Explanation

Let initial mass =` m_(Q)`
Since fuel is 90% of total mass
:.mass of container, `m_(c) = m_(0) -(90)/(100)m_(0)`
`m_(c)=(1)/(10)m_(0)`
`:.(m_(0))/(m_(c))=10`
Now burnt out speed
`upsilon_(b)=ulog_(e)(m_(0))/(m_(c))=2.303u log_(10)10`
`=2.303xx1000xx1=2303m//s=2.3 kms^(-1)`
Hence correct choice is (a)