intro
Question 1:
What is the computed angular velocity of our planet, Earth?
Topic: Angular Velocity in Planetary Motion
Correct Answer: A) 2π/86400 rad/sec
- Angular Velocity is a measure of the rate of change in angle per unit time. It's essential in understanding planetary motion.
- For Earth, the angular velocity is calculated considering its one full rotation completed in 24 hours. This time is converted into seconds for better computation.
- Therefore, Earth's time to complete one revolution = t = 24 hours = 24 × 60 × 60 = 86400 seconds.
- Hence, using the angular velocity formula (ω = 2π/t), we find that Earth's angular velocity is 2π/86400 rad/sec.
Question 2:
What is the equivalent degree measurement for one radian?
Topic: Radians to Degrees Conversion
Correct Answer: B) 57.3°
- Radian is a unit of angular measurement.
- When converted into degrees, 1 radian is approximately equal to 57.3 degrees.
Question 3:
What is Earth's daily rotational angular speed in rad s-1?
Topic: Angular Speed in Earth's Rotation
Correct Answer: D) 7.3×10-5 rad-1
- Angular speed is a measure of how quickly an object moves through an angle.
- This speed is represented as 7.3×10-5 rad-1 for the Earth's daily rotation.
Question 4:
How many degrees does one complete revolution represent?
Topic: Revolution Degrees
Correct Answer: B) 360°
- A revolution is a full rotation around a circle.
- In terms of degrees, one complete revolution equals 360 degrees.
Question 5:
Assuming the orbit to be circular, how many days would make up a year if we halve the current distance between Earth and the Sun?
Topic: Orbital Period and Distance
Correct Answer: D) 129 days
- The orbital period of a planet is determined by its distance from the sun, as per Kepler's Third Law which states that a planet's semi-major axis equals the square of its period (T² + r³).
- We can use this relation to calculate the new period if the distance is halved. The resulting equation (365/T₂)² = (2r₁/r₁)³ simplifies to (365/T₂)² = 8.
- Solving this equation gives us T₂ = 365 / (2√2) which results in approximately 129 days. Hence, the correct answer is D, "129 days".
Question 6:
What physical aspect is measured using a tachometer?
Topic: Tachometer Usage
Correct Answer: C) Rotational speed
- A tachometer is an instrument used to gauge the rotational speed of a mechanical component, often displayed in revolutions per minute (RPM).
- Effective in various applications such as automobiles, aircraft, and boats, the tachometer provides critical information about the functioning speed of these components.
Question 7:
Under which type of force is the angular momentum conserved?
Topic: Conservation of Angular Momentum
Correct Answer: B) Central Force
- Angular momentum conservation is a fundamental concept in physics, it states that if no external torque acts on a system, the total angular momentum remains constant.
- This principle is notably applicable under central forces, which are forces oriented towards a common center.
- Hence, the correct answer is B, "Central Force".
Question 8:
A geosynchronous satellite completes its full orbit around the Earth in what timeframe?
Topic: Geosynchronous Satellite Orbits
Correct Answer: D) 24 hours
- A geosynchronous satellite is one that revolves around the Earth in such a manner that from a fixed point on Earth, the satellite appears to be stationary.
- This type of satellite completes one full orbit around the Earth in a 24-hour period, hence keeping pace with the Earth's rotation.
Question 9:
How can we best approximate the radius of a geostationary orbit from the Earth's center?
Topic: Geostationary Orbit Radius
Correct Answer: A) 42000 km
- A geostationary orbit, which is a type of geosynchronous orbit, lies on the plane of the Earth’s equator.
- The approximated radius of this orbit, measured from the Earth's center, extends to about 42,164 km.
- Hence, the correct answer is A, "42000 km".
Question 10:
For a body that performs two complete revolutions around a circle with radius 'R', what would be the ratio of its displacement to the path covered?
Topic: Circular Motion Displacement
Correct Answer: C) Zero
- In the context of circular motion, displacement refers to the shortest distance from the starting point to the ending point.
- If a body performs two complete revolutions around a circle, then its starting and ending points coincide. Therefore, the displacement is zero.
- Hence, the correct answer is C, "Zero".
Question 11:
What is the work done by the centripetal force?
Topic: Centripetal Force and Work
Correct Answer: D) No work
- Centripetal force is the force that keeps a body moving along a circular path, acting at all times perpendicular to the direction of the body's motion.
- As work is defined as the force multiplied by the distance over which it acts, and the direction of work is the same as that of motion, work done by a force perpendicular to the motion is zero.
- Therefore, the correct answer is D, "No work".
Question 12:
What is the standard unit of angular displacement in the International System of Units (SI)?
Topic: Angular Displacement in SI Units
Correct Answer: D) Radian
- When a point or line is rotated about an axis, it creates an angle.
- In the International System of Units (SI), the standard unit of angular displacement is the radian.
- Therefore, the correct answer is D, "Radian".
Question 13:
One degree is equivalent to how many radians?
Topic: Degrees to Radians Conversion
Correct Answer: A) 0.01745
- In the field of trigonometry, it's common to convert between degrees and radians.
- Specifically, one degree is equal to π/180 radians, which is approximately 0.01745 radians.
- Therefore, the correct answer is A, "0.01745".
Question 14:
Who is credited with the formulation of the inverse square law of gravitation?
Topic: Gravitational Inverse Square Law
Correct Answer: C) Newton
- Gravitational forces can be explained mathematically by the inverse square law of gravity.
- A mass's gravitational force is inversely proportional to its distance from its center.
- This groundbreaking principle is attributed to Isaac Newton, making the correct answer C, "Newton".
Question 15:
How many complete revolutions correspond to an angular displacement of 3π radians?
Topic: Revolutions and Radians
Correct Answer: C) 3/2
- In circular motion, a full revolution corresponds to an angular displacement of 2π radians.
- To find the number of revolutions corresponding to an angular displacement of 3π radians, we divide the given radians by the radians of a full revolution (2π).
- Therefore, the number of revolutions for 3π radians is 3π/2π = 3/2, making the correct answer C, "3/2".
Question 16:
What celestial body has a weight at the Earth's surface of about 9.8 N/kg?
Topic: Gravitational Acceleration
Correct Answer: D) Earth
- The weight of an object on a celestial body's surface is determined by the force of gravity acting on it.
- On Earth, the gravitational acceleration is about 9.8 m/s^2, which means that an object's weight at the surface of this planet is approximately 9.8 N/kg (Newton per kilogram).
- Therefore, the correct answer is D, "Earth".