Q: A vector $$ \vec{A} $$ has components $$ A_x = 3 $$ and $$ A_y = 4 . $$What is the magnitude and direction (relative to the x-axis) of $$ \vec{A} $$?

$$A = \sqrt{3^2$ + 4^2$} = 5$$, \theta = \$$tan^{-1}(4/3$$) \approx 53.1^\circ$

Q: The efficiency of a heat engine is given by $$e = \frac{\text{what you get}}{\text{what you had to pay}}. $$For a Carnot engine, what is the maximum efficiency in terms of the hot and cold reservoir temperatures?

$$e_{\text{max}} = 1 - \frac{T_C}{T_H}$$

Question 1

A vector $$ \vec{A} $$ has components $$ A_x = 3 $$ and $$ A_y = 4 . $$What is the magnitude and direction (relative to the x-axis) of $$ \vec{A} $$?

Accepted Answer

$$A = \sqrt{3^2$ + 4^2$} = 5$$, 	heta = \$$tan^{-1}(4/3$$) \approx 53.1^\circ$

Question 2

Which shape has the smallest moment of inertia for rotation about its center, given equal mass and radius?

Accepted Answer

Solid sphere: $$I = \frac{2}{5}MR^2$

Question 3

A steel rod of length $$L$$ and cross-sectional area $$A is $$stretched by a force $$F$$, causing an extension $$\Delta L. $$Which equation relates these quantities to Young's modulus $$Y$$?

Accepted Answer

$$F = Y \frac{A \Delta L}{L}$$

Question 4

A rolling object has both translational and rotational kinetic energy. Which equation correctly expresses its total kinetic energy?

Accepted Answer

$$K = \frac{1}{2}mv^2$ + \frac{1}{2}I\$$omega^2$$

Question 5

The efficiency of a heat engine is given by $$e = \frac{	ext{what you get}}{	ext{what you had to pay}}. $$For a Carnot engine, what is the maximum efficiency in terms of the hot and cold reservoir temperatures?

Accepted Answer

$$e_{	ext{max}} = 1 - \frac{T_C}{T_H}$$

Question 6

A gas in a cylinder undergoes an isothermal expansion from $$V_i to$$ $$V_f. $$Which area on the $$p$$-$$V$$ diagram represents the work done by the gas?

Accepted Answer

The area under the curve between $$V_i$$ and $$V_f$$

Question 7

For an ideal gas, which equation relates pressure, volume, and temperature for $$N$$ molecules and $$n$$ moles?

Accepted Answer

$$pV = Nk_B T$$ and $$pV = nRT$$

Question 8

A mass attached to a spring oscillates with amplitude $$A$$ and frequency $$f. $$What is the equation for its position as a function of time?

Accepted Answer

$$x(t) = A \cos(2\pi f t)$$

Question 9

In a pipe with varying cross-sectional area, the flow rate $$Q is $$constant. Which equation correctly relates the velocities and areas at two points?

Accepted Answer

$$Q = v_1$ A_1$ = v_2$ A_2$

Question 10

A sound source moves toward a stationary observer. Which equation describes the observed frequency shift due to the Doppler effect?

Accepted Answer

$$\Delta f = +2 f_s \frac{V_0$}{V}$$

Question 11

For thin film interference, which condition results in constructive interference when there is one phase change?

Accepted Answer

$$2t = (m + \frac{1}{2}) \frac{\lambda}{n}$$

Question 12

A converging lens forms a real image. Which statement is correct about the image?

Accepted Answer

The image is inverted and on the opposite side of the lens from the object.

Question 13

The resolving power of a microscope is determined by the minimum distance $$d_{min}$$ between two points. Which equation expresses $$d_{min}$$?

Accepted Answer

$$d_{min} = \frac{0.61 \lambda}{NA}$$

Question 14

The angular resolution $$\$$theta_1$$ of a telescope is given by which equation?

Accepted Answer

$$\$$theta_1$$ = \frac{1.22 \lambda}{D}$$

Question 15

A loop of area $$A is $$placed in a magnetic field $$B at an $$angle $$	heta. $$What is the magnetic flux through the loop?

Accepted Answer

$$\Phi = AB \cos 	heta$$

Question 16

The right-hand rule is used to determine the direction of the force on a charged particle moving in a magnetic field. Which finger represents the velocity vector?

Accepted Answer

The middle finger

Question 17

The Stefan-Boltzmann constant $$\sigma is $$used in the equation for blackbody radiation. What is its value and units?

Accepted Answer

$$\sigma = 5.67 	imes 10$$^{-8}$$ \frac{W}{m^2$ K^4$}$$

Question 18

The peak wavelength $$\lambda_{peak} of $$blackbody radiation is given by Wien's law. Which equation is correct?

Accepted Answer

$$\lambda_{peak} = \frac{2.9 	imes 10^6$ 	ext{ nm} \cdot K}{T}$$

Comprehensive Physics Equations and Concepts: Chapters 1–30

Study Guide - Practice Questions

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