Question-59347

Question Number 59347 by Tinkutara last updated on 08/May/19

Commented by Tinkutara last updated on 08/May/19

B part only

Commented by Tinkutara last updated on 09/May/19

Yes I am too sad with mine also. Got 4.5k. Yours? But I don't think it's a mistake by NTA, it's an era of tough competition!

Commented by Tinkutara last updated on 09/May/19

Mine was 230 One of my friend got 300 marks but 2.6k AIR What was your marks?

Commented by rahul 19 last updated on 09/May/19

201. U r very lucky! 4530 at 230 marks !!! as far as I know for a rank under 5,000 ,you need 260+ ...

Commented by Tinkutara last updated on 09/May/19

But marks have no meaning now. I got 290 in April but low percentile so January marks were considered. Tmhari kabki %ile maani hai?

Commented by prakash jain last updated on 10/May/19

What shift you were in April ?

9 th April morning ?

All other shift would have fetched

you rank under 2 k with 290 marks

Commented by Tinkutara last updated on 10/May/19

Yes 9th morning in April

Answered by ajfour last updated on 09/May/19

Commented by ajfour last updated on 11/May/19

m \frac{dv}{dt} = - \sqrt{2 gh} \frac{dm}{dt} (as m \frac{dv}{dt} = v_{rel} \frac{dm}{dt} + F_{ext})

(ρ Ah) \frac{dv}{dt} = - \sqrt{2 gh} [\frac{d}{dt} (ρ Ah)]

\frac{dv}{dt} = - \sqrt{2 g} \times \frac{1}{\sqrt{h}} \frac{dh}{dt} \dots . (i)

further

- \frac{A}{100} \sqrt{2 g \frac{H}{4}} = A \frac{dh}{dt}

or \frac{dh}{dt} = - \frac{1}{100} \sqrt{\frac{gH}{2}}

\frac{dv}{dt} = \sqrt{2 g} \times \frac{2}{\sqrt{H}} \times \frac{1}{100} \sqrt{\frac{gH}{2}}

a = \frac{g}{50}

And from (i)

dv = - \sqrt{2 g} \times \frac{dh}{\sqrt{h}}

v = 2 \sqrt{2 g} (\sqrt{H} - \sqrt{h})

when h = \frac{H}{4}

v = \sqrt{2 gH} = \sqrt{\frac{{2 m}_{0} g}{ρ A}} .

Commented by Tinkutara last updated on 12/May/19

as m \frac{dv}{dt} = v_{rel} \frac{dm}{dt} + F_{ext}

P l e a s e e x p l a i n t h i s S i r .

Commented by ajfour last updated on 12/May/19

consider a rocket entering an

atmosphere and accumulating

mass as it proceeds;

let rocket speed be v,

External force acting F_{ext}

mass dm of atmosphere, moving

at speed u, and

rocket of mass m be our system,

p_{i} = udm + mv

p_{f} = (m + dm) (v + dv)

dp = (v - u) dm + mdv

F_{ext} dt + (u - v) dm = mdv

\Rightarrow \frac{m d v}{d t} = v_{r e l} \frac{d m}{d t} + F_{e x t} .

Commented by Tinkutara last updated on 13/May/19

Thank you Sir!