26 reviewed questions with answers and explanations.
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An object is projected at 80 m/s,30° above horizontal. Neglect air resistance and use g =10 m/s². Find its maximum height above the launch point.
B: 80 m
The initial upward velocity is 80 sin 30° =40 m/s. At maximum height the vertical velocity is zero, so h =40²/(2 ×10) =80 m.
AI-reviewed · calculation checkedA particle moves in a fixed horizontal circle at constant angular velocity. Which statement is true?
A: Kinetic energy is constant but linear momentum varies
At constant angular velocity on a fixed circle, speed is constant, so kinetic energy stays constant. The direction of velocity changes continuously, making linear momentum change direction.
AI-reviewed · source checkedA uniform horizontal beam of weight 200 N and length 50 m is pivoted at one end. A cord at the other end makes 30° above the beam and holds it in equilibrium. Find the cord tension.
D: 200 N
Taking moments about the pivot, the cord contributes T sin 30° ×L while the uniform beam’s weight contributes 200 ×L/2. Thus T ×0.5 =100, giving T =200 N.
AI-reviewed · calculation checkedA 50 kg object is released from rest 2 m above the ground. Neglect air resistance and use g =10 m/s². Find its kinetic energy just before impact.
B: 1 000 J
Neglecting air resistance, gravitational potential energy becomes kinetic energy. Thus K =mgh =50 ×10 ×2 =1000 J just before impact.
AI-reviewed · calculation checkedA horizontal force just starts a 20 kg object sliding on a horizontal surface. The coefficient of static friction is 0.2. Find the force, using g = 10 m/s².
B: 40.0 N
Just before sliding starts, the limiting friction is μₛN. The horizontal force leaves N = mg, so F = 0.2 × 20 × 10 = 40 N.
AI-reviewed · calculation checkedFor a connected liquid of uniform density at rest, neglecting capillary effects, which statements are true? I. Pressure acts equally in all directions at a point. II. Pressure decreases with depth. III. Pressure at the same horizontal level is the same. IV. Pressure depends on the cross-sectional area of a barometer tube.
A: I and III only.
At a point in a liquid at rest, pressure acts equally in every direction. In a connected liquid of uniform density, equal depths have equal pressure. Pressure increases with depth and does not depend on tube area.
AI-reviewed · source checkedThe mass of a specific gravity bottle is 15.2 g when it is empty. It is 24.8 g when filled with kerosene and 27.2 g when filled with distilled water. Calculate the relative density of kerosene.
D: 0.80
The kerosene mass is 24.8 − 15.2 = 9.6 g, and the water mass is 27.2 − 15.2 = 12.0 g. Equal bottle volumes give relative density 9.6/12.0 = 0.80.
AI-reviewed · calculation checkedIf a solid X floats in liquid P of relative density 2.0 and in liquid Q of relative density 1.5, it can be inferred that the
D: Volume of P displaced is less than that of Q
A floating object displaces its own weight of either liquid. Since P is denser, less of it is needed to provide that weight: Vₚ/Vq = 1.5/2.0 = 0.75.
AI-reviewed · calculation checkedConvert 78 °C to kelvin, to the nearest kelvin.
B: 351 K
Convert Celsius to kelvin by adding 273.15. Thus 78 °C is 351.15 K, which rounds to 351 K to the nearest kelvin.
AI-reviewed · calculation checkedMix 100 g of liquid L₁ at 78 °C with X grams of liquid L₂ at 50 °C. The final temperature is 66 °C. The specific heat capacity of L₂ is half that of L₁. Neglect heat loss and container heat capacity. Find X.
C: 150 g
Heat lost equals heat gained: 100 c(78 − 66) = X(c/2)(66 − 50). Therefore 1200 c = 8 Xc, so X = 150 g.
AI-reviewed · calculation checkedA heater melts 100 g of ice at its melting point in 1 minute. Neglect heat losses and the test tube’s heat capacity. Find its power. Use latent heat of fusion 336 J/g.
C: 560 W
Melting requires Q = mL = 100 × 336 = 33600 J. One minute is 60 s, so the required power is Q/t = 33600/60 = 560 W.
AI-reviewed · calculation checkedA transverse wave is y = 0.3 sin(0.5 x − 50 t), where x and y are in centimetres, t is in seconds, and the phase is in radians. What is the maximum displacement magnitude?
D: 0.3 cm
In y = A sin(kx − ωt), the sine varies between −1 and 1. The largest displacement magnitude is therefore A = 0.3 cm.
AI-reviewed · calculation checkedSound travels from the surface to the sea bottom and returns after 4 s. If its speed is 1500 m/s, find the depth.
B: 3000 m
The echo makes a return trip, travelling twice the sea depth. Thus d = vt/2 = 1500 × 4/2 = 3000 m.
AI-reviewed · calculation checkedWhich change halves the fundamental frequency of a stretched sonometer wire, with other relevant quantities held constant?
A: Double its vibrating length at fixed tension and mass per unit length
For a stretched wire, f = (1/2 L)√(T/μ), where μ is mass per unit length. Doubling the vibrating length while holding tension and μ fixed halves the fundamental frequency.
AI-reviewed · calculation checkedA stretched string has fundamental frequency 400 Hz. Its vibrating length is doubled and its tension quadrupled, with mass per unit length unchanged. Find the new frequency.
B: 400 Hz
Fundamental frequency is proportional to √T/L at fixed mass per unit length. The new frequency is 400 × √4/2 = 400 Hz.
AI-reviewed · calculation checkedTo produce a parallel paraxial beam from a concave mirror, where should a small lamp be placed on its principal axis?
A: One focal length from the mirror
A small lamp at a concave mirror’s principal focus sends rays that reflect parallel to the principal axis in the paraxial approximation. Its distance is therefore the focal length.
AI-reviewed · source checkedLight of frequency 6.0 × 10¹⁴ Hz enters stationary glass of refractive index 1.5 from air. Find its frequency in the glass.
B: 6.0 × 10¹⁴ Hz
A stationary boundary does not change the light’s frequency. In glass, speed and wavelength decrease together, leaving frequency at 6.0 × 10¹⁴ Hz.
AI-reviewed · source checkedA converging thin lens of focal length 20 cm forms a virtual image with magnification 2. Find the object distance.
B: 10 cm
For an upright virtual image of magnification 2, v = −2 u. The thin-lens equation gives 1/20 =1/u −1/(2 u) =1/(2 u), so u =10 cm.
AI-reviewed · calculation checkedAn object touches the bottom of a glass block 3.0 cm thick, with refractive index 1.5. Viewed from air nearly normally through the top face, by how much does the object appear raised?
A: 1.0 cm
For near-normal viewing through a plane glass surface, apparent depth is real depth divided by refractive index:3.0/1.5 =2.0 cm. The object appears raised by 3.0 −2.0 =1.0 cm.
AI-reviewed · calculation checkedA projection lantern uses a converging lens of focal length f to make a real enlarged image on a screen. Its object distance u must satisfy
D: f < u < 2 f
A projector needs a real enlarged image on a screen. A converging lens produces that image when the object is farther than f but nearer than 2 f.
AI-reviewed · source checkedA plastic pen rubbed with dry silk attracts a small piece of paper. What happens to the pen and cloth during rubbing?
D: Both the pen and the cloth are charged.
Rubbing transfers electric charge between the pen and cloth, leaving opposite charges on them. The charged pen polarizes nearby neutral paper, and the nearer opposite charge is attracted more strongly.
AI-reviewed · source checkedResistors R₁ =4 Ω and R₂ =5 Ω are in parallel across the same voltage. Find P₁:P₂.
B: 5:4
Parallel resistors have the same voltage. Since P = V²/R, their power ratio is P₁/P₂ = R₂/R₁ =5/4, giving 5:4.
AI-reviewed · calculation checkedA cell of emf 12 V and internal resistance 1 Ω supplies two parallel resistors, 12 Ω and 6 Ω. Find the magnitude of current in the 12 Ω resistor.
A: 0.8 A
The parallel equivalent is 12 ×6/(12 +6) =4 Ω. Including internal resistance gives 5 Ω, so total current is 12/5 =2.4 A. Terminal voltage is 2.4 ×4 =9.6 V, giving 9.6/12 =0.8 A in the 12 Ω resistor.
AI-reviewed · calculation checkedIf two parallel conductors carry currents flowing in the same direction, the conductors will
A: Attract each other
Each conductor produces a magnetic field at the other. Applying the magnetic-force direction rule to parallel currents in the same direction gives a force on each wire toward the other.
AI-reviewed · source checkedA sinusoidal alternating voltage has frequency 50 Hz. P is an upward zero crossing and R is the immediately following downward zero crossing. Find the time from P to R.
C: 1/100 s
Consecutive zero crossings with opposite slopes are half a cycle apart. At 50 Hz, a cycle lasts 1/50 s, so the interval is 1/100 s.
AI-reviewed · calculation checkedIn the ordinary single-photon photoelectric effect, light of photon energy 2 eV falls on a metal of work function 3 eV. What happens?
A: No photoelectron is emitted
A photon must supply at least the work function to liberate an electron. Here 2 eV is less than 3 eV, so ordinary single-photon photoemission does not occur.
AI-reviewed · source checked