All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
3541
Find the angular velocity of the earth rotating on its axis, in radians per hour.
Answer:
π/12
The earth completes one full rotation (2π radians) in approximately 24 hours. Therefore, its angular velocity is 2π / 24 = π/12 radians per hour.
3542
What is the area of a circle if a sector of central angle π/4 has an area of 10 cm²?
Answer:
80 cm²
A full circle has an angle of 2π radians. The given sector is a fraction of the circle: (π/4) / 2π = 1/8 of the circle. Since the sector area is 10 cm², the total area of the circle is 10 * 8 = 80 cm².
3543
The ratio of the radii of two circles is 3:4. If they subtend the same angle at their respective centers, what is the ratio of their arc lengths?
Answer:
3:4
Arc length l is proportional to the radius r for a constant angle θ (l = rθ). Therefore, the ratio of their arc lengths is exactly the same as the ratio of their radii, which is 3:4.
3544
Convert the angle 5π/12 radians into sexagesimal units (degrees).
Answer:
75°
To convert to degrees, substitute 180° for π: (5 * 180°) / 12 = 5 * 15° = 75°.
3545
What is the angle subtended by a chord of length equal to the radius of the circle at the center?
Answer:
π/3 radians
If the chord length equals the radius, the triangle formed by the two radii and the chord is an equilateral triangle. Every angle in an equilateral triangle is 60°, which converts exactly to π/3 radians.
3546
Find the length of the arc intercepted by a central angle of 40° in a circle of radius 18 cm.
Answer:
4π cm
Convert 40° to radians: 40 * (π/180) = 2π/9 rad. Now use l = rθ: l = 18 * (2π/9) = 2 * 2π = 4π cm.
3547
A bicycle wheel rotates 10 times per second. How many radians does it rotate through in 5 seconds?
Answer:
100π
One rotation equals 2π radians. 10 rotations per second equals 20π radians per second. In 5 seconds, the wheel rotates through 20π * 5 = 100π radians.
3548
If an arc of length 15π cm subtends an angle of 3π/4 radians, find the diameter of the circle.
Answer:
40 cm
Use the formula l = rθ. Here l = 15π and θ = 3π/4. 15π = r * (3π/4). Dividing both sides by π gives 15 = r * 3/4. Multiplying by 4/3 gives r = 15 * 4 / 3 = 20 cm. The diameter is 2r = 40 cm.
3549
Convert the angle 11° 15' into radians.
Answer:
π/16
First, convert to decimal degrees: 11° + (15/60)° = 11° + 0.25° = 11.25°. Now, multiply by π/180: 11.25 * (π/180) = 45/4 * (π/180) = π / (4 * 4) = π/16 radians.
3550
If a car's tire has a radius of 30 cm and rotates at 10 rad/s, what is the linear speed of the car?
Answer:
3 m/s
The relationship between linear speed (v), radius (r), and angular speed (ω) is v = rω. First convert r to meters: r = 30 cm = 0.3 m. Then, v = 0.3 m * 10 rad/s = 3 m/s.