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Word: apple

Definition: A fruit that is typically round and red, green, or yellow.

MCQ SET 01 Physics Class 11

Section – A: Multiple Choice Questions

Question 1:

Which of the following is the correct representation of a 10 cm long scale?

(A) The scale of the length is 10 cm.
(B) This is a 10 cm long scale.
(C) This is a 10 cm long scale.
(D) The scale of the length is 10 c.m.

Answer: (A) The scale of the length is 10 cm.

Explanation: Units should be symbolically represented without dots unless they appear at the end of a sentence as a full stop.

Question 2:

The displacement (in meters) of a body varies with time t (in seconds) as x = t² - 2t - 3. The displacement is zero for a positive value of t equal to:

(A) 1 s
(B) 4 s
(C) 3 s
(D) 2 s

Answer: (C) 3 s

Explanation: Given x = t² - 2t - 3. For x = 0, 0 = (t + 1)(t - 3) so t = 3, -1.

Question 3:

If A = B + C and the magnitudes of A, B, and C are 5, 4, and 3, respectively, then the angle between A and C is:

(A) sin^-1 (3/5)
(B) cos^-1 (3/5)
(C) cos^-1 (4/5)
(D) sin^-1 (4/5)

Answer: (B) cos^-1 (3/5)

Question 4:

Application of lubricants cannot reduce:

(A) Static friction
(B) Sliding friction
(C) Rolling friction
(D) Inertia

Answer: (D) Inertia

Question 5:

A force of 49 N is just able to move a block of mass 10 kg on a rough horizontal surface. The coefficient of friction is:

(A) 0.5
(B) 1.0
(C) 0
(D) 0.8

Answer: (A) 0.5

Question 6:

When a body is dropped from a tower, then there is an increase in its:

(A) Weight
(B) Acceleration
(C) Velocity
(D) Gravitational potential energy

Answer: (C) Velocity

Question 7:

A cyclist comes to a skidding stop in 20 m. During this process, the force on the cycle due to the road is 100 N and is directly opposed to the motion. Work done by the road on the cycle is:

(A) -2000 J
(B) 2000 J
(C) 1000 J
(D) 100 J

Answer: (A) -2000 J

Question 8:

On which of the following factors does the moment of inertia of an object not depend?

(A) Axis of rotation
(B) Angular velocity
(C) Distribution of mass
(D) Mass of an object

Answer: (B) Angular velocity

Question 9:

Escape velocity of an object of mass m is proportional to:

(A) m²
(B) m
(C) m^-1
(D) m⁰

Answer: (D) m⁰

Question 10:

Rigidity modulus and Young’s modulus are respectively η and Y. A copper wire of length L and area of cross-section A is pulled so that its length becomes 5L and area of cross-section becomes A/5. So:

(A) Y increases, η decreases.
(B) η increases, Y decreases.
(C) Both Y and η increase.
(D) Both Y and η remain unchanged.

Answer: (D) Both Y and η remain unchanged.

Kepler's laws of motion

Kepler's Laws of Planetary Motion

Johannes Kepler, a German mathematician and astronomer, formulated three fundamental laws to describe the motion of planets in the 17th century. These laws provided a revolutionary understanding of planetary orbits, moving away from the ancient belief in perfect circular orbits to elliptical orbits. Let’s explore each of Kepler's Laws in detail:

1. Kepler's First Law: The Law of Ellipses

The First Law states that planets move in elliptical orbits with the Sun at one focus of the ellipse. Mathematically, this can be expressed as:

r = ^{a(1 − e²)} / _{1 + e cos θ}

where r is the distance of the planet from the Sun, a is the semi-major axis of the ellipse, e is the eccentricity of the orbit, and θ is the angle from the closest approach to the Sun.

2. Kepler's Second Law: The Law of Equal Areas

The Second Law, or the Law of Equal Areas, describes how a line segment joining a planet and the Sun sweeps out equal areas in equal intervals of time. This means that when a planet is closer to the Sun, it travels faster, and when it is farther from the Sun, it travels slower. The mathematical expression for the area swept per unit time (angular momentum) is:

dA / dt = ¹/₂ r² dθ / dt = constant

where dA is the area swept out, r is the distance to the Sun, and dθ/dt is the rate of change of the angle.

3. Kepler's Third Law: The Law of Harmonies

The Third Law establishes a relationship between the distance of a planet from the Sun and its orbital period. According to this law, the square of a planet’s orbital period (T) is proportional to the cube of the semi-major axis (a) of its orbit:

T² ∝ a³

This can also be written as:

T² = k a³

where k is a constant that depends on the mass of the Sun. This law allowed astronomers to predict the motion of planets with greater accuracy.

Explore Kepler's Laws in Animation

To better visualize these laws, you can view an animation that demonstrates Kepler’s Laws in action. Visit the following link to see the planetary motions and how each law applies to them:

Click here to view animation of Kepler's Laws of Planetary Motion

Kepler’s Laws not only transformed our understanding of the Solar System but also laid the groundwork for Newton’s Law of Gravitation, further enhancing our comprehension of celestial mechanics.

By understanding these laws, we gain insight into the structure and order of our Solar System, as well as the mechanics that govern planetary bodies across the universe.

Kepler's Laws of planetary motion

Understanding Kepler's Laws of Planetary Motion

Kepler's Laws of Planetary Motion describe how planets move around the sun. These laws, formulated by the German astronomer Johannes Kepler in the early 17th century, are foundational for understanding orbits in our solar system and beyond. Below is an animation demonstrating each of Kepler's laws in action. The animation includes a planet orbiting the sun and a satellite orbiting that planet.

Kepler's Laws in Action

Kepler's Laws in Action

Kepler's First Law: Elliptical orbit with the Sun at one focus.

Kepler's Second Law: Equal areas swept in equal times.

Kepler's Third Law: Relationship between distance and orbital period.

Explanation of Kepler's Laws

Kepler's First Law: The Law of Ellipses

According to Kepler's First Law, planets orbit the Sun in an elliptical path, with the Sun located at one of the foci of the ellipse. This means that the distance between the planet and the Sun varies throughout the orbit, contrary to the earlier belief that planets move in perfect circles.

Kepler's Second Law: The Law of Equal Areas

Kepler's Second Law states that a line segment connecting a planet to the Sun sweeps out equal areas during equal intervals of time. This means that when a planet is closer to the Sun, it moves faster, and when it is farther from the Sun, it moves slower. This law helps explain why planets speed up near the Sun and slow down as they move away.

Kepler's Third Law: The Law of Harmonies

Kepler's Third Law establishes a relationship between the orbital period of a planet and its average distance from the Sun. Specifically, the square of a planet's orbital period (the time it takes to complete one orbit) is directly proportional to the cube of the semi-major axis of its orbit. This law shows that planets further from the Sun take much longer to complete an orbit than planets that are closer.