A hot air balloon is carrying some passengers, and a few sandbags… - Vidyadip

MCQ

A hot air balloon is carrying some passengers, and a few sandbags of mass $1 kg$ each so that its total mass is $480 kg$. Its effective volume giving the balloon its buoyancy is $V$. The balloon is floating at an equilibrium height of $100 m$. When $N$ number of sandbags are thrown out, the balloon rises to a new equilibrium height close to $150 m$ with its volume $V$ remaining unchanged. If the variation of the density of air with height $h$ from the ground is $\rho(h)=\rho_0 e^{-\frac{h}{h_0}}$, where $\rho_0=1.25 kg m ^{-3}$ and $h _0=6000 m$, the value of $N$ is. . . . .

A
$3$
✓
$4$
C
$5$
D
$6$

✓

Answer

Correct option: B.

$4$

b
$480 \times g=v \rho_1 g$

$(480-N) g=v \rho_2 g$

$\frac{480-N}{480}=\frac{\rho_2}{\rho_1}$

$\left(1-\frac{N}{480}\right)=\frac{e^{-h_2 / h_0}}{e^{-h_1 / h_0}}=e^{\frac{h_1-h_2}{h_0}}=e^{-\frac{50}{6000}}$

$1-\frac{N}{480}=1-\frac{50}{6000} \Rightarrow N=\frac{50 \times 480}{6000}=4$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 9.1 , fluid mechanics→9.1 , fluid mechanics — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A particle is moving in a circle with uniform speed. Its motion is

A man balances himself in a horizontal position by pushing his hands and feet against two parallel walls. His centre of mass lies midway between the walls. The coefficients of friction at the walls are equal. Which of the following is not correct?

The door of a running refrigerator inside a room is left open. The correct statement out of the following ones is:

In the figure, the ball $A$ is released from rest when the spring is at its natural (unstretched) length. For the block $B$ of mass $M$ to leave contact with the ground at some stage, the minimum mass of $A$ must be

From the top of a tower two stones, whose masses are in the ratio $1 :2$ are thrown one straight up with an initial speed $u$ and the second straight down with the same speed $u$. Then, neglecting air resistance

The atmospheric pressure and height of barometer column is $10^5\,Pa$ and $760\,mm$ respectively on the Earth surface. If the barometer is taken to the Moon then column height will be ........ $mm$

From the top of a tower of height $40\,m$, a ball is projected upwards with a speed of $20\,m / s$ at an angle of elevation of $30^{\circ}$. The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (take $g=10\,m / s ^2$ )

If two systems are in thermal equilibrium with each other, it means their:

A train moves towards a stationary observer with speed $34\, m/s$. The train sounds a whistle and its frequency registered by the observer is $f_1$. If the speed of the train is reduced to $17\, m/s$, the frequency registered is $f_2$. If speed of sound is $340\, m/s$, then the ratio $f_1/f_2$ is

Two bodies of masses $m$ and $4\,m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is