Chapter 14: Q77P (page 412)

A glass ball of radius $2.00 c m$ sits at the bottom of a container of milk that has a density of $1.03 g / c m^{3}$ . The normal force on the ball from the container’s lower surface has magnitude $9.48 \times 10^{- 2} N$ . What is the mass of the ball?

Short Answer

Expert verified

The mass of the ball is $0.0442 k g$ .

Step by step solution

Listing the given quantities

Radius of the ball $(r) = 2 \times 10^{- 2} m$ .
Normal force, $N = 9.48 \times 10^{- 2} N$ .
The density of milk,

$\begin{array}{rcl} (ρ_{m}) & = & 1.03 g / c m^{3} \\ = & 1030 k g / m^{3} \end{array}$

Understanding the concept of buoyant force

There are three forces acting on the bubble –buoyant force $(F_{b})$ ,weight,and normal reaction.As the ball is stationary, the net force acting on the ball is zero. Using this concept, we can find

Formula:

$F_{n e t} = 0 F_{b} = M_{b} g = ρ_{b} V_{b} g W = M_{b} g V = \frac{4}{3} π r^{3}$

(a) Calculation of mass of the ball

The volume of the milk displaced by the ball(Vmilk) = Volume of the ball (Vb)

$\begin{array}{rcl} V_{m i l k} & = & \frac{4}{3} π r^{3} \\ = & \frac{4}{3} \times 3.14 \times {(2 \times 10^{- 2} m)}^{3} \\ = & 33.472 \times 10^{- 6} m^{3} \end{array}$

Using Newton’s second law,

$N + F_{b} - - W = 0 N + ρ_{m} V_{b} g - - M_{b} g = 0$

Rearranging the equation,

$M_{b} = \frac{N + ρ_{m} V_{b} g}{g}$

Substitute the values in the above equation.

$= \frac{9.48 \times 10^{- 2} N+ (1030 {kg/m}^{3} × (33.472 × 10^{- 6} m^{3}) × 9.8 \frac{m}{s^{2}})}{9.8 \frac{m}{s^{2}}}$

Therefore, the mass of the ballis $0.0442 k g$ .

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A glass ball of radius $2.00 c m$ sits at the bottom of a container of milk that has a density of $1.03 g / c m^{3}$ . The normal force on the ball from the container’s lower surface has magnitude $9.48 \times 10^{- 2} N$ . What is the mass of the ball?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concept of buoyant force

(a) Calculation of mass of the ball

One App. One Place for Learning.

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A glass ball of radius 2.00cmsits at the bottom of a container of milk that has a density of 1.03g/cm3. The normal force on the ball from the container’s lower surface has magnitude 9.48×10-2N. What is the mass of the ball?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concept of buoyant force

(a) Calculation of mass of the ball

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Translational Dynamics

Conservation of Energy and Momentum

Astrophysics

Oscillations

Waves Physics

Study anywhere. Anytime. Across all devices.

A glass ball of radius $2.00 c m$ sits at the bottom of a container of milk that has a density of $1.03 g / c m^{3}$ . The normal force on the ball from the container’s lower surface has magnitude $9.48 \times 10^{- 2} N$ . What is the mass of the ball?