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A balloon with mass 'm' is descending down with an acceleration 'a' (where a<g). How much mass should be removed from it so that it starts moving up with an acceleration 'a'?

Option 1)
$\frac{2ma}{g+a}$

Option 2)
$\frac{2ma}{g-a}$

Option 3)
$\frac{ma}{g+a}$

Option 4)
$\frac{ma}{g-a}$

Answers (1)

best_answer

As we learnt in

Newton's 2nd Law -

$F\propto \frac{dp}{dt}$

$F=\tfrac{kdp}{dt}$

$F=\tfrac{d\left (mv \right )}{dt}$

$F=\tfrac{m\left (dv \right )}{dt}$

$\frac{dv}{dt}=a$

Therefore $F=ma$

- wherein

$K=1$ in C.G.S & S.I

When ballon descending down

$Mg-F_{v}=ma-------(i)$

$F_{v}$ = upthrust force

When ballon moving up

$F_{v}-(m- \lambda m)g=(m- \lambda m)a-------(ii)$

$\therefore$ from equations (i) and (ii) we get

$\lambda m = \frac{2ma}{g+a}$

Option 1)

$\frac{2ma}{g+a}$

This option is correct.

Option 2)

$\frac{2ma}{g-a}$

This option is incorrect.

Option 3)

$\frac{ma}{g+a}$

This option is incorrect.

Option 4)

$\frac{ma}{g-a}$

This option is incorrect.

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Plabita

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