SATHEE: Laws of Motion - Result Question 24

Laws of Motion - Result Question 24

24. 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’?

[2014]

(a) $\frac{2 m a}{g + a}$

(b) $\frac{2 m a}{g - a}$

(d) $\frac{m a}{g - a}$

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Answer:

Correct Answer: 24. (a)

Solution:

(a) Let upthrust of air be $F_{a}$ then For downward motion of balloon,

$F_{a} = m g - m a \Rightarrow F a = m (g - a)$

For upward motion,

$\begin{matrix} (ii) & F_{a} - (m - Δ m) g = (m - Δ m) a \end{matrix}$

From equation (i) and (ii),

Therefore, $Δ m = \frac{2 m a}{(g + a)}$

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Laws of Motion - Result Question 24

24. 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’?

Answer:

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24. 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’?