Question

Example 3.10 A ball of mass 2kg has a diameter of 50cm falls in the pool. Calculate its buoyant force and volume of water displaced. sition - th​

Answer 1

Answer:

• Buoyant force = 19.6N
• Water displaced = 0.065m³

Explanation:

Question says that,

A ball of mass 2kg had a diameter of 50cm falls in a pool.

Calculate it's buoyant force and volume of the water displaced.

Here,

$\implies {\rm W_f }= mg$

Where,

• $\rm W_f$ denotes the weight of the fluid.
• $m$ is the mass of the ball.
• $g$ is the acceleration due to gravity = 9.8m/s

From the given values,

$\implies \rm W_f =(2 )\ast(9.8)$

$\implies \rm W_f =19.6N$

According to the Archimedes' principal, When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

Hence, the buoyant force is 19.6N

Also,

Calculating the water displacement.

So here,

→ Water displaced = Volume occupied by the ball.

Since it's a sphere.

Volume of the ball is given by,

$= \dfrac{4}{3} \pi {r}^{3}$

We have,

• diameter of the ball = 50cm or, 0.5m [On conversion to S.I. unit]
• so the radius $(r) = \dfrac{0.5}{2}\rm m$

$= \dfrac{4}{3} \times \dfrac{22}{7} \times { \bigg(\dfrac{0.5}{2} \bigg)}^{3}$

$= \dfrac{4}{3} \times \dfrac{22}{7} \times \dfrac{0.125}{8}$

$= \dfrac{4}{3} \times \dfrac{22}{7} \times \dfrac{125}{8000}$

$\rm = 0.065 {m}^{3}$

__________________________

Answer 2

Answer:

Given :-

• A ball of mass 2 kg has a diameter of 50 cm falls in the pool.

To Find :-

• What is the buoyant force and volume of water displaced.

Formula Used :-

$\clubsuit$ Weight Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{W =\: m \times g}}}\: \: \: \bigstar$

where,

• W = Weight (N)
• m = Mass (kg)
• g = Acceleration due to gravity (m/s²)

$\clubsuit$ Volume of Sphere Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Volume_{(Sphere)} =\: \dfrac{4}{3}{\pi}r^3}}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius

Solution :-

First, we have to find the buoyant force :-

Given :

• Mass = 2 kg
• Acceleration due to gravity = 9.8 m/s²

According to the question by using the formula we get,

$\implies \bf W =\: m \times g$

$\implies \sf W =\: 2 \times 9.8$

$\implies \sf\bold{\purple{W =\: 19.6\: N}}$

Hence, the buoyant force is 19.6 N

Now, we have to find the volume of water displaced :

First, we have to find the radius :

Given :

• Diameter = 50 cm

According to the question by using the formula we get,

$\implies \bf Radius =\: \dfrac{Diameter}{2}$

$\implies \sf Radius =\: \dfrac{50}{2}$

$\implies \sf\bold{\green{Radius =\: 25\: cm}}$

Now, we have to find the volume of water :

Given :

• Pie (π) = 22/7
• Radius (r) = 25 cm = 0.25 m

According to the question by using the formula we get,

$\implies \bf Volume_{(Ball)} =\: \dfrac{4}{3}{\pi}r^3$

$\implies \sf Volume_{(Ball)} =\: \dfrac{4}{3} \times \dfrac{22}{7} \times (0.25)^3$

$\implies \sf Volume_{(Ball)} =\: \dfrac{4 \times 22}{3 \times 7} \times (0.25 \times 0.25 \times 0.25)$

$\implies \sf Volume_{(Ball)} =\: \dfrac{88}{21} \times 0.015625$

$\implies \sf Volume_{(Ball)} =\: \dfrac{1.375}{21}$

$\implies \sf\bold{\red{Volume_{(Ball)} =\: 0.065\: m^3}}$

$\therefore$ The buoyant force is 19.6 N and the volume of water displaced is 0.065 m³ .