A spring with spring constant k = 100 N/m is compressed by 0.1 m. What is the elastic potential energy stored?
A
0.5 J
B
1 J
C
5 J
D
10 J
Explanation:
Elastic PE = ½kx² = ½ × 100 × (0.1)² = ½ × 100 × 0.01 = 0.5 J.
A block slides down a frictionless incline of angle 30°. What is its acceleration down the incline?
A
5 m/s²
B
8.66 m/s²
C
9.8 m/s²
D
10 m/s²
Correct Answer:
A. 5 m/s²
Explanation:
On a frictionless incline, a = g sin(θ) = 10 × sin(30°) = 10 × 0.5 = 5 m/s².
Two identical objects moving with velocities v and 2v collide and stick together. What fraction of kinetic energy is lost?
Explanation:
Initial KE = ½m(v)² + ½m(2v)² = 2.5mv². Final velocity = 3v/2 (by momentum conservation). Final KE = ½(2m)(3v/2)² = 2.25mv²/4 = 0.84mv². Loss = 2.5 - 0.84 = 1.66, which is 2/3 of initial KE.
A conducting sphere is given a charge of 8 μC. What is the electric field at its surface if the radius is 2 cm?
A
1.8 × 10⁶ N/C
B
3.6 × 10⁷ N/C
C
1.8 × 10⁷ N/C
D
7.2 × 10⁷ N/C
Correct Answer:
C. 1.8 × 10⁷ N/C
Explanation:
Electric field at surface: E = kQ/r² = (9 × 10⁹ × 8 × 10⁻⁶)/(0.02)² = (72)/(4 × 10⁻⁴) = 1.8 × 10⁷ N/C.
A submarine sonar uses ultrasound with frequency 50 kHz and speed 1500 m/s in water. What is the wavelength?
A
0.03 m
B
0.3 m
C
3 m
D
30 m
Correct Answer:
A. 0.03 m
Explanation:
Wavelength λ = v/f = 1500/(50 × 10³) = 1500/50000 = 0.03 m = 3 cm. Higher frequencies in denser mediums produce shorter wavelengths.
An object undergoes simple harmonic motion with amplitude 5 cm and frequency 2 Hz. What is the maximum velocity?
A
10π cm/s
B
20π cm/s
C
5π cm/s
D
2.5π cm/s
Correct Answer:
B. 20π cm/s
Explanation:
Maximum velocity in SHM: v_max = ωA = 2πfA = 2π × 2 × 5 = 20π cm/s ≈ 62.8 cm/s.
A radioactive element has a half-life of 10 years. What fraction of the original sample remains after 30 years?
Explanation:
After 30 years = 3 half-lives: N = N₀ × (1/2)³ = N₀/8. The sample reduces by half three times successively.
A 10 m long ladder leans against a vertical wall at 60° to the ground. How high does it reach on the wall?
A
5 m
B
5√3 m
C
10√3 m
D
10/√3 m
Explanation:
Height = L × sin(60°) = 10 × (√3/2) = 5√3 m ≈ 8.66 m. The vertical component of the ladder's length is found using trigonometry.
A concave mirror has a focal length of 20 cm. An object is placed at 40 cm from the mirror. What type of image is formed?
A
Virtual, erect, magnified
B
Real, inverted, same size
C
Virtual, erect, diminished
D
Real, inverted, diminished
Correct Answer:
B. Real, inverted, same size
Explanation:
Object at 2f (40 cm = 2 × 20 cm) forms image at 2f. Using mirror equation confirms v = 40 cm, m = -1 (real, inverted, same size as object).
A wire of length L and cross-sectional area A has resistance R. If the wire is cut into two equal halves and connected in parallel, what is the new resistance?
Explanation:
Each half has resistance R/2. When connected in parallel: 1/R_new = 1/(R/2) + 1/(R/2) = 4/R, so R_new = R/4.
