Q: A car moves along a straight road with a constant acceleration. If its initial velocity is $$u = 5\ \text{m/s}$$ and its acceleration is $$a = 2\ \text{m/s}^2$$, what is the displacement after $$t = 4\ \text{s}$$?

$$s = u t + \frac{1}{2} a t^2$ = 5 \times 4 + \frac{1}{2} \times 2 \times 16 = 20 + 16 = 36\ \text{m}$$

Q: A projectile is launched at an angle $$\theta = 30^\circ$$ with an initial speed $$v_0 = 20$$\ \text{m/s}$$. What is the maximum height reached by the projectile? (Take g = 10$$\ \text{m/s}^2$$)

$$H = \frac{v_0$^2 \sin^2$ \theta}{2g} = \frac{20^2$ \times (\frac{1}{2})^2$}{2 \times 10} = \frac{400 \times 0.25}{20} = \frac{100}{20} = 5\ \text{m}$$

Q: A block of mass $$m = 2\ \text{kg} is $$placed on a rough horizontal surface. If the coefficient of static friction is $$\mu_s = 0.4$$, what is the minimum force required to start moving the block? (Take $$g = 9.8\ \text{m/s}^2)$$

$$F_{\text{min}} = \mu_s m g = 0.4 \times 2 \times 9.8 = 7.84\ \text{N}$$

Q: A satellite is in a circular orbit around the Earth at a height where the acceleration due to gravity is $$g' = 8\ \text{m/s}^2. If $$the radius of the orbit is $$r = 7000\ \text{km}$$, what is the orbital speed of the satellite?

$$v = \sqrt{g' r} = \sqrt{8 \times 7 \times 10^6$} = \sqrt{56 \times 10^6$} \approx 7483\ \text{m/s}$$

Q: A spring with spring constant $$k = 200\ \text{N/m} is $$compressed by $$x = 0.1\ \text{m}. $$What is the potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times 0.01 = 1\ \text{J}$$

Q: A rigid body rotates with angular velocity $$\omega = 10\ \text{rad/s}$$ and has a moment of inertia $$I = 5\ \text{kg}\cdot\text{m}^2. $$What is its angular momentum?

$$L = I \omega = 5 \times 10 = 50\ \text{kg}\cdot\text{m}^2/\text{s}$$

Q: A metal rod of length $$l = 2\ \text{m} is $$subjected to a force $$F = 1000\ \text{N}$$ and has a cross-sectional area $$A = 0.01\ \text{m}^2. If $$its Young's modulus is $$Y = 2 \times 10^7$\ \text{N/m}^2$$, what is the elongation $$\Delta l$$?

$$\Delta l = \frac{F l}{A Y} = \frac{1000 \times 2}{0.01 \times 2 \times 10^7$} = \frac{2000}{2 \times 10^5$} = 0.01\ \text{m}$$

Q: A $$500\ \text{g}$$ block of ice at $$0^\circ\text{C} is $$placed in $$100\ \text{g} of $$water at $$40^\circ\text{C}. If $$the latent heat of fusion is $$L_f = 80,000\ \text{J/kg}$$ and specific heat of water is $$c = 4,200\ \text{J/kg}\cdot\text{K}$$, will all the ice melt? (Assume no heat loss)

Heat required to melt ice: $$Q_1 = m$$_{\text{ice}} L_f = 0.5 \times 80,000 = 40,000\ \text{J}$$; Heat available from water: Q_2$ = m_{\text{water}} c \Delta T = 0.1 \times 4,200 \times 40 = 16,800\ \text{J}$$; Since $$Q_2$$ \u003c $$Q_1$$, not all ice will melt.

Q: A sound wave travels through air with a frequency $$f = 500\ \text{Hz}$$ and wavelength $$\lambda = 0.68\ \text{m}. $$What is the speed of sound in air?

$$v = f \lambda = 500 \times 0.68 = 340\ \text{m/s}$$

Q: A resistor of $$R = 10\ \Omega is $$connected to a $$12\ \text{V}$$ battery. What is the current flowing through the resistor?

$$I = \frac{V}{R} = \frac{12}{10} = 1.2\ \text{A}$$

Question 1

A car moves along a straight road with a constant acceleration. If its initial velocity is $$u = 5\ 	ext{m/s}$$ and its acceleration is $$a = 2\ 	ext{m/s}^2$$, what is the displacement after $$t = 4\ 	ext{s}$$?

Accepted Answer

$$s = u t + \frac{1}{2} a t^2$ = 5 	imes 4 + \frac{1}{2} 	imes 2 	imes 16 = 20 + 16 = 36\ 	ext{m}$$

Question 2

A projectile is launched at an angle $$	heta = 30^\circ$$ with an initial speed $$v_0 = 20$$\ 	ext{m/s}$$. What is the maximum height reached by the projectile? (Take g = 10$$\ 	ext{m/s}^2$$)

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ 	heta}{2g} = \frac{20^2$ 	imes (\frac{1}{2})^2$}{2 	imes 10} = \frac{400 	imes 0.25}{20} = \frac{100}{20} = 5\ 	ext{m}$$

Question 3

A block of mass $$m = 2\ 	ext{kg} is $$placed on a rough horizontal surface. If the coefficient of static friction is $$\mu_s = 0.4$$, what is the minimum force required to start moving the block? (Take $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$F_{	ext{min}} = \mu_s m g = 0.4 	imes 2 	imes 9.8 = 7.84\ 	ext{N}$$

Question 4

A satellite is in a circular orbit around the Earth at a height where the acceleration due to gravity is $$g' = 8\ 	ext{m/s}^2. If $$the radius of the orbit is $$r = 7000\ 	ext{km}$$, what is the orbital speed of the satellite?

Accepted Answer

$$v = \sqrt{g' r} = \sqrt{8 	imes 7 	imes 10^6$} = \sqrt{56 	imes 10^6$} \approx 7483\ 	ext{m/s}$$

Question 5

A spring with spring constant $$k = 200\ 	ext{N/m} is $$compressed by $$x = 0.1\ 	ext{m}. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes 0.01 = 1\ 	ext{J}$$

Question 6

A rigid body rotates with angular velocity $$\omega = 10\ 	ext{rad/s}$$ and has a moment of inertia $$I = 5\ 	ext{kg}\cdot	ext{m}^2. $$What is its angular momentum?

Accepted Answer

$$L = I \omega = 5 	imes 10 = 50\ 	ext{kg}\cdot	ext{m}^2/	ext{s}$$

Question 7

A metal rod of length $$l = 2\ 	ext{m} is $$subjected to a force $$F = 1000\ 	ext{N}$$ and has a cross-sectional area $$A = 0.01\ 	ext{m}^2. If $$its Young's modulus is $$Y = 2 	imes 10^7$\ 	ext{N/m}^2$$, what is the elongation $$\Delta l$$?

Accepted Answer

$$\Delta l = \frac{F l}{A Y} = \frac{1000 	imes 2}{0.01 	imes 2 	imes 10^7$} = \frac{2000}{2 	imes 10^5$} = 0.01\ 	ext{m}$$

Question 8

A $$500\ 	ext{g}$$ block of ice at $$0^\circ	ext{C} is $$placed in $$100\ 	ext{g} of $$water at $$40^\circ	ext{C}. If $$the latent heat of fusion is $$L_f = 80,000\ 	ext{J/kg}$$ and specific heat of water is $$c = 4,200\ 	ext{J/kg}\cdot	ext{K}$$, will all the ice melt? (Assume no heat loss)

Accepted Answer

Heat required to melt ice: $$Q_1 = m$$_{	ext{ice}} L_f = 0.5 	imes 80,000 = 40,000\ 	ext{J}$$; Heat available from water: Q_2$ = m_{	ext{water}} c \Delta T = 0.1 	imes 4,200 	imes 40 = 16,800\ 	ext{J}$$; Since $$Q_2$$ \u003c $$Q_1$$, not all ice will melt.

Question 9

A sound wave travels through air with a frequency $$f = 500\ 	ext{Hz}$$ and wavelength $$\lambda = 0.68\ 	ext{m}. $$What is the speed of sound in air?

Accepted Answer

$$v = f \lambda = 500 	imes 0.68 = 340\ 	ext{m/s}$$

Question 10

A resistor of $$R = 10\ \Omega is $$connected to a $$12\ 	ext{V}$$ battery. What is the current flowing through the resistor?

Accepted Answer

$$I = \frac{V}{R} = \frac{12}{10} = 1.2\ 	ext{A}$$

Question 11

A convex lens has a focal length $$f = 20\ 	ext{cm}. An $$object is placed $$u = -30\ 	ext{cm}$$ from the lens. What is the image distance $$v$$?

Accepted Answer

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \Rightarrow \frac{1}{20} = \frac{1}{v} - \frac{1}{-30} \Rightarrow \frac{1}{v} = \frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{5}{60} \Rightarrow v = 12\ 	ext{cm}$$

Question 12

A wire carries a current $$I = 5\ 	ext{A}$$ and is placed perpendicular to a magnetic field $$B = 0.2\ 	ext{T}. If $$the length of the wire in the field is $$l = 0.5\ 	ext{m}$$, what is the force on the wire?

Accepted Answer

$$F = B I l = 0.2 	imes 5 	imes 0.5 = 0.5\ 	ext{N}$$

Question 13

A capacitor of $$C = 10\ \mu	ext{F} is $$charged to a potential difference $$V = 100\ 	ext{V}. $$What is the energy stored in the capacitor?

Accepted Answer

$$U = \frac{1}{2} C V^2$ = \frac{1}{2} 	imes 10 	imes 10$$^{-6}$$ 	imes 100^2$ = 0.05\ 	ext{J}$$

Question 14

A monochromatic light of wavelength $$\lambda = 600\ 	ext{nm}$$ passes through a double slit with separation $$d = 0.2\ 	ext{mm}. $$What is the angular position $$	heta of $$the first bright fringe?

Accepted Answer

$$\sin 	heta = \frac{\lambda}{d} = \frac{600 	imes 10$$^{-9}$$}{0.2 	imes 10$$^{-3}$$} = 3 	imes 10$$^{-3}$$

Question 15

A radioactive sample has a half-life of $$T_{1/2} = 10\ 	ext{days}. $$What fraction of the sample remains after $$30\ 	ext{days}$$?

Accepted Answer

After $$n = \frac{30}{10} = 3$$ half-lives, fraction remaining $$= \left(\frac{1}{2}\$$right)^3$$ = \frac{1}{8}$$

Question 16

A simple pendulum has a length $$l = 1\ 	ext{m}. $$What is its period of oscillation? (Take $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$T = 2\pi \sqrt{\frac{l}{g}} = 2\pi \sqrt{\frac{1}{9.8}} \approx 2\pi 	imes 0.32 \approx 2.01\ 	ext{s}$$

Question 17

A transformer has a primary coil with $$N_p = 1000$$ turns and a secondary coil with $$N_s = 100$$ turns. If the input voltage is $$V_p = 220\ 	ext{V}$$, what is the output voltage $$V_s$$?

Accepted Answer

$$V_s = V_p \frac{N_s}{N_p} = 220 	imes \frac{100}{1000} = 22\ 	ext{V}$$

Question 18

A person lifts a $$20\ 	ext{kg}$$ box to a height of $$2\ 	ext{m} in$$ $$5\ 	ext{s}. $$What is the power expended?

Accepted Answer

Work done $$W = m g h = 20 	imes 9.8 	imes 2 = 392\ 	ext{J}$$; Power $$P = \frac{W}{t} = \frac{392}{5} = 78.4\ 	ext{W}$$

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