Question

Exercise 1: A hot-air balloon has a volume of 440 x 10"3
m"3. Calculate the buoyant force that the surrounding cold
air exerts on the balloon? Given that the density of the
surrounding air is 2.58 kg/m"3.

Answer 1

Given:

A hot-air balloon has a volume of 440 x 10³ m³.

To Find:

Calculate the buoyant force that the surrounding cold  air exerts on the balloon? Given that the density of the  surrounding air is 2.58 kg/m³.

Solution:

Buoyant force exerted by air on balloon can be find out by using the formula, which are given below:

$\mathbf{Buoyant \ Force = F_{b}= \rho _{a}\times V_{d}\times g}$

Where:

$\mathbf{\rho _{a}= Density\ of\ air = 2.58 \ \ \dfrac{kg}{m^{3}}}$

$\mathbf{V_{d}=\textrm{Volume displaced by balloon} = 440\times 10^{3} \ \ \ m^{3}}$

$\mathbf{g=\textrm{Gravitational acceleration} = 10 \ \ \ \dfrac{m}{s^{2}}}$

On putting respective value in equation of buoyant force:

$\mathbf{Buoyant \ Force = F_{b}= \rho _{a}\times V_{d}\times g}$

$\mathbf{Buoyant \ Force = F_{b}= 2.58\times 440\times 10^{3}\times 10}$

$\mathbf{Buoyant \ Force = F_{b}= 11352000 \ \ \ \ N}$

Means force exerted by cold air on balloon is 11352000 N.

Answer 2

$\large \green{ \fcolorbox{gray}{black}{ ☑ \: \textbf{Verified \: answer}}}$

Means force exerted by cold air on balloon is 11352000 N.