Points to remember in physics - Part 11

Points to remember in physics - Part 11

101. The speed of a particle cannot be negative 

Speed is a scalar quantity that refers to the magnitude of an object's velocity. It is always a positive value or zero. Speed cannot be negative because it only describes the magnitude of motion, not the direction of motion. 

However, velocity is a vector quantity that takes into account both the magnitude and direction of motion. Velocity can be negative when the object is moving in the opposite direction of a chosen positive direction. For example, if we choose the positive x-axis as the direction of motion, an object moving towards the left (negative x direction) will have a negative velocity.

102. The x-t graph cannot take sharp turns

In most cases, the x-t graph represents the position of an object as a function of time. Since an object's position cannot change instantaneously, the x-t graph cannot have sharp turns or corners. Any changes in position must occur gradually over time and be represented by a smooth curve on the graph.

103. A particle cannot have two velocities at an instant.

At a given instant, a particle can only have one velocity. Velocity is a vector quantity that has both a magnitude (speed) and a direction. It describes how fast an object is moving and in what direction it is moving. 

If a particle changes its direction of motion at an instant, its velocity will change as well. However, it can only have one velocity vector at a time. This means that if a particle is moving in a straight line, it will have a single velocity vector that describes its speed and direction of motion. Similarly, if a particle is moving in a curved path, its velocity vector will change as it moves along the path, but it will always have a single velocity vector at any given instant.

It's worth noting that a particle can have different velocities at different instants, but not at the same instant.

104. A particle cannot have two displacements at on instant.

At a given instant, a particle can only have one displacement vector. Displacement is a vector quantity that describes the change in position of an object from an initial position to a final position. 

If a particle changes its direction of motion at an instant, its displacement vector will change as well. However, it can only have one displacement vector at a time. This means that at any given instant, the particle will have a single displacement vector that describes the distance and direction between its current position and its initial position.

It's worth noting that a particle can have different displacements at different instants, but not at the same instant.

105. The value of current in a short circuit is infinite.

A short circuit occurs when there is a direct connection between the positive and negative terminals of a power source, bypassing the normal load or resistance. 

In this situation, the impedance of the circuit becomes extremely low, approaching zero.

According to Ohm's Law (V = I × R), when the resistance (R) approaches zero, the current (I) theoretically becomes infinite, provided the voltage (V) remains constant. 

This concept is often used in idealized circuit analysis to simplify calculations and understand the behavior of circuits under short circuit conditions.

106. Acceleration can be seen in a rotating frame of reference.

In physics, a frame of reference is a coordinate system used to describe the motion of objects. 

When the frame of reference is rotating, the laws of physics can appear different compared to an inertial frame of reference (a frame that is not accelerating or rotating).

In a rotating frame of reference, objects may experience a centrifugal force and a Coriolis force. 

The centrifugal force is a pseudo-force that appears to act outward from the center of rotation. It is experienced by objects in the rotating frame and can give the appearance of an acceleration away from the center of rotation.

The Coriolis force, on the other hand, is a pseudo-force that acts perpendicular to the velocity of a moving object in a rotating frame. 

It can cause an object to experience a deflection or a change in its trajectory. 

The Coriolis force is responsible for various phenomena, such as the rotation of weather patterns on Earth and the deviation of moving objects on rotating platforms.

107. Copper has low electrical resistivity.

Copper is known for its low electrical resistivity, which means it is an excellent conductor of electricity. 

(Electrical resistivity is a property that quantifies a material's resistance to the flow of electric current). 

Copper has one of the lowest electrical resistivities among common metals, making it a preferred choice for a wide range of electrical applications.

The low electrical resistivity of copper is due to its atomic structure and the behavior of its electrons. Copper has a relatively high number of free electrons in its outermost energy level, which are loosely bound and can move freely through the material when a voltage is applied. This enables efficient conduction of electricity, as the free electrons can easily carry electric charge from one point to another.

Because of its low resistivity, copper is extensively used in various electrical and electronic systems. It is commonly used in electrical wiring for buildings, power transmission and distribution lines, motors, generators, transformers, and printed circuit boards (PCBs). Its excellent conductivity helps minimize energy losses and ensures efficient power transmission and utilization.

108. Acceleration of earth around the sun in its orbit is always tangential.

The acceleration of the Earth around the Sun in its orbit is always tangential.

In orbital motion, an object moves in a curved path due to the gravitational force exerted by a central body. 

For the Earth orbiting the Sun, the gravitational force provides the necessary centripetal force to keep the Earth in its orbit. 

According to Newton's laws of motion, when an object moves in a curved path, there must be an acceleration directed toward the center of the curve, known as the centripetal acceleration.

In the case of the Earth's orbit around the Sun, the centripetal acceleration is always directed toward the center of the orbit, which is the Sun. 

Since the Earth's orbit is nearly circular, the centripetal acceleration is always perpendicular to the radius vector that connects the Earth to the Sun. 

In other words, the centripetal acceleration is always tangential to the Earth's orbit.

This tangential acceleration helps maintain the Earth's orbital speed and keeps it moving in a stable orbit around the Sun. 

The gravitational force provides the necessary centripetal acceleration, keeping the Earth in a continuous state of acceleration toward the Sun while maintaining its orbital path.

It's important to note that while the acceleration is always tangential, its magnitude remains constant since the Earth's orbit is nearly circular and the gravitational force between the Earth and the Sun is relatively constant. 

This allows the Earth to maintain a stable orbit with a relatively constant distance from the Sun over long periods of time.

109. Work done by friction can be positive or negative.

The work done by friction can be positive or negative, depending on the specific situation.

Friction is a force that opposes the relative motion or tendency of motion between two surfaces in contact. When an object slides or moves against a surface with friction, work is done by or against the frictional force.

1. Positive Work: If the direction of the applied force and the direction of the frictional force are the same, the work done by friction is positive. In this case, the applied force is doing work to overcome the frictional resistance, resulting in energy transfer from the object to the surface. For example, when pushing a box across a floor, the applied force is in the same direction as the frictional force, and work is done by friction, converting the object's energy into heat.

2. Negative Work: If the direction of the applied force and the direction of the frictional force are opposite, the work done by friction is negative. In this case, the frictional force acts in the opposite direction to the applied force, reducing the object's energy or resisting its motion. For example, when an object slides down a slope, gravity provides a downward force while friction acts in the opposite direction. The work done by friction is negative as it acts against the motion of the object, removing energy from the system.

It's important to note that the magnitude of the work done by friction is given by the product of the magnitude of the frictional force and the displacement of the object in the direction of the force. 

The positive or negative sign indicates the direction of energy transfer or removal.

110. Misconception: The angle between radius vector and centripetal acceleration is "π".

The angle between the radius vector and the centripetal acceleration is not π (pi) radians. The angle between the radius vector and the centripetal acceleration is actually 90 degrees, or π/2 radians.

In circular motion, the centripetal acceleration is always directed toward the center of the circle, while the radius vector points from the center of the circle to the object moving in the circular path. These two vectors are perpendicular to each other, forming a right angle.

The centripetal acceleration is responsible for changing the direction of the object's velocity, keeping it in the circular path. The radius vector, on the other hand, represents the position of the object relative to the center of the circle.

So, the angle between the radius vector and the centripetal acceleration is 90 degrees or π/2 radians. This perpendicular relationship between the two vectors is crucial in understanding the dynamics of circular motion.

111. The role of Inductance is equal to inertia.

Explanation:

The role of inductance in electrical circuits can be compared to the role of inertia in mechanical systems, although they are not exactly equivalent concepts.

Inertia is a property of matter in which an object tends to resist changes in its velocity. It is related to the mass of an object, where objects with greater mass have greater inertia.

Inductance, on the other hand, is a property of electrical circuits that describes the ability of a circuit element (typically an inductor) to resist changes in the current flowing through it. 

Inductance is a result of the electromagnetic phenomenon called self-induction, which occurs when the magnetic field associated with a changing current induces an electromotive force (EMF) that opposes the change in current.

While inertia and inductance share the concept of resisting changes, they are different in nature. Inertia is a property of matter related to mass, while inductance is a property of electrical circuits related to the flow of electric current and the creation of magnetic fields.

That being said, the effect of inductance in electrical circuits can be analogously compared to inertia in mechanical systems. Like inertia, inductance resists changes in the flow of current. It tends to oppose sudden changes in current by creating an opposing EMF, just as inertia resists changes in velocity. Inductance plays a role in maintaining the stability of electrical systems and can impact the behavior of circuits during transients and changes in current.

112. Atmosphere around the earth held by gravity

Yes, the atmosphere around the Earth is held in place by the force of gravity. Gravity is the force that pulls all objects with mass towards each other, and it is what keeps the Earth orbiting around the Sun. The Earth's gravity also keeps the atmosphere from escaping into space.

The atmosphere is made up of a mixture of gases, including nitrogen, oxygen, carbon dioxide, and others. These gases are constantly moving and colliding with each other and with the Earth's surface. The force of gravity keeps the gases close to the surface of the Earth, creating the pressure that we experience as atmospheric pressure.

Without gravity, the atmosphere would simply float away into space, leaving the Earth without the protective layer of gases that shields us from the harsh conditions of space and provides the air that we breathe.

113. An arc of length equal to the circumference of a circle subtends an angle of 2π radian.

Yes.

An arc of length equal to the circumference of a circle will subtend an angle of 2π radians at the center of the circle.

To see why this is true, consider a circle of radius r. The circumference of the circle is given by the formula 2πr, which represents the total distance around the edge of the circle. Now imagine taking an arc of length 2πr from the edge of the circle. This arc would stretch exactly halfway around the circle, from one side to the other.

Since the circumference of the circle is equal to the length of the arc, we know that the angle subtended by this arc at the center of the circle must be equal to the angle subtended by the full circumference of the circle, which is 2π radians.

114. Misconception:

Instantaneous velocity is positive. 

Instantaneous velocity can indeed be positive. In physics, velocity is a vector quantity that describes both the speed and direction of an object's motion. 

Positive velocity indicates that an object is moving in the positive direction of a chosen coordinate system.

For example, if a car is moving in a straight line towards the right, and you consider the rightward direction as positive, then the instantaneous velocity of the car will be positive. It indicates that the car is moving in the positive direction of the coordinate system at that particular moment.

However, it's important to note that instantaneous velocity can change over time. So, while it may be positive at one instant, it could become negative or zero at another instant, depending on the direction and speed of the object's motion.

115. Concept: The maximum power delivered by the battery is Pmax=E²/4r.

The formula you provided, Pmax = E²/4r, represents the maximum power delivered by a battery in a circuit, where E represents the electromotive force (EMF) of the battery and r represents the internal resistance of the battery.

This formula is derived from the concept of maximum power transfer theorem in electrical circuits. According to this theorem, the maximum power is transferred from a source (in this case, a battery) to a load (connected to the battery) when the load resistance is equal to the internal resistance of the source.

In the formula, E represents the EMF of the battery, which is the voltage provided by the battery when no current is flowing. The term E² represents the square of the EMF.

The term 4r represents four times the internal resistance of the battery.

Dividing E² by 4r yields the maximum power that can be delivered by the battery to the load when the load resistance is equal to the internal resistance of the battery.

It's important to note that this formula assumes ideal conditions and neglects other factors that may affect the actual power delivery in a real-world scenario, such as losses due to wiring resistance, efficiency, and limitations of the battery chemistry.

▪️Derivation:

To derive the formula for the maximum power delivered by a battery, we'll use the concept of maximum power transfer theorem.

The maximum power transfer theorem states that the maximum power is transferred from a source (in this case, a battery) to a load (connected to the battery) when the load resistance is equal to the internal resistance of the source. In this case, we'll assume that the load resistance is equal to the internal resistance of the battery.

Let's consider a circuit with a battery of electromotive force (EMF) E and internal resistance r connected to a load resistor R. The current flowing through the circuit is given by Ohm's Law:

I = (E - V) / (r + R),

where I is the current flowing through the circuit and V is the voltage across the load resistor.

The power delivered to the load resistor is given by:

P = V * I.

To find the maximum power delivered to the load resistor, we need to maximize P with respect to R. To do this, we differentiate P with respect to R and set the derivative equal to zero:

dP/dR = V * (dI/dR) + I * (dV/dR) = 0.

Since dV/dR = 0 (as the voltage across the load resistor does not depend on its own resistance), we can simplify the equation to:

V * (dI/dR) = 0.

Now, let's differentiate I with respect to R:

dI/dR = - (E - V) / (r + R)².

Substituting this into our previous equation, we have:

V * (-(E - V) / (r + R)²) = 0.

Simplifying further:

V * (E - V) = 0.

Expanding the equation:

VE - V² = 0.

Rearranging the equation to solve for V:

V² - VE = 0.

Factoring out V:

V * (V - E) = 0.

This equation implies that either V = 0 or V = E.

If V = 0, then there is no current flowing through the load resistor, which means no power is delivered. Thus, it is not the maximum power.

If V = E, then the voltage across the load resistor is equal to the EMF of the battery. In this case, the power delivered to the load resistor is:

P = V * I = E * (E / (r + R)) = E² / (r + R).

To find the maximum power, we need to set R equal to r, which represents the internal resistance of the battery:

Pmax = E² / (r + r) = E² / (2r).

Simplifying further:

Pmax = E² / 2r = E² / 4r * 2 = E² / 4r.

Therefore, we have derived the formula for the maximum power delivered by a battery: Pmax = E² / 4r.

116. According to wien's law, temperature and wave length are inversely related.

According to Wien's displacement law, there is an inverse relationship between the temperature of an object and the wavelength at which the object emits the maximum intensity of radiation.

Wien's displacement law is mathematically represented as:

λ_max = b / T,

where λ_max is the wavelength at which the object emits the maximum intensity of radiation, T is the temperature of the object in Kelvin, and b is Wien's displacement constant.

The constant b in the equation is approximately equal to 2.898 × 10^(-3) meters per Kelvin. It is a proportionality constant that relates the temperature and the peak wavelength of the blackbody radiation emitted by an object.

From the equation, we can see that as the temperature T increases, the wavelength λ_max at which the object emits the maximum intensity of radiation decreases. In other words, higher temperature objects emit radiation at shorter wavelengths, such as visible light or even shorter wavelengths like ultraviolet or X-rays.

Conversely, as the temperature T decreases, the wavelength λ_max at which the object emits the maximum intensity of radiation increases. Lower temperature objects emit radiation at longer wavelengths, such as infrared or even longer wavelengths like radio waves.

So, indeed, according to Wien's law, temperature and wavelength are inversely related.