### Air enclosed in a sphere has density 1.4 kg/m^3. What will the density be if the radius of the sphere is halved, compressing the air within?

The main purpose of this question is to find the density of the air enclosed in the sphere if the radius of the sphere is halved. A sphere is a  $3-$dimensional body with a circular shape. It is divided into three $x-$axis, the $y-$axis, and the $z-$axis. This is the primary distinction between a sphere […]

### Using the two equations E=hv and c=lambda v derive an equation expressing E in terms of h,c and lambda.

This question aims to express the quantum of energy $(E)$ in terms of the speed of light $(c)$, the wavelength $(lambda)$, and Planck’s constant $(h)$. The frequency can be expressed as the number of oscillations in one unit of time and it is calculated in Hz (hertz). The wavelength is regarded as the measure of […]

### A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by x(t)=bt^2-ct^3, where b=2.40 m/s^2 and c=0.120 m/s^3. (a) Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. (b) Calculate the instantaneous velocity of the car at t=0, t = 5.0 s, and t = 10.0 s. (c) How long after starting from rest is the car again at rest?

This article aims to find a car’s average and instantaneous velocity at times. This article uses the concept of average velocity. Average velocity is the change in position $(Delta x)$ divided by the time intervals $(Delta t)$ in which the displacement occurs. Average velocity can be negative or positive depending on the sign of the shift. […]

### A potter’s wheel having a radius of 0.50 m and a moment of inertia of 12 kg m^2 is rotating freely at 50 rev/min. The potter can stop the wheel in 6.0 s by pressing a wet rag against the rim and exerting a radially inward force of 70 N. Find the effective coefficient of kinetic friction between the wheel and the wet rag.

This question aims to find the coefficient of kinetic friction between the wheel and the wet rag. The opposition of any substantial body to its velocity change is defined as inertia. This involves changes in the direction of movement or the speed of the body. The moment of inertia is a quantifiable measure of a body’s rotational inertia, which […]

### What is the total surface charge qext on the exterior surface of the conductor?

– In a conducting sphere with a neutral charge, there exists a hollow cavity inside it in the form of a sphere. There is a point charge present at the center of the spherical cavity having a positive charge $q$. – (A) For the given conductor, find the total charge $q_{int}$ that exists on its […]

### A hammer in an out-of-tune piano.

This question aims to find the highest and lowest frequency of the string of an out-of-tune piano. The hammer of this piano hits two strings and produces a beat of 7 Hz and one of the strings of this piano is tuned to 131 Hz. The number of waves passing through a fixed point in […]

### An element of atomic number 88 decays radioactively to an element of atomic number 82.

Given the following four types of possible emissions, which one achieves the given result? A pair of alpha and beta particles A single alpha particle A group of three alpha particles A group of six beta particles The aim of this question is to learn the fundamental types of nuclear decay. There are basically three […]

### When the current i is positive, the capacitor charge q is decreasing.

From the given Figure, answer the questions either True or False based on the circuit’s behavior: – After the RELAY is switched to either the N.O. (“normally open”) or N.C. (“normally closed”) state, the transient response of the circuit is for the short time. – In this experiment, the transient current flow has an exponential […]

### A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of 41 g. What is the density of the steel in g/cm^3?

This question aims to find the density of the cylinder walls. A solid three-dimensional shape made up of two parallel bases connected by a curved surface is called a cylinder. Both of the bases are shaped like circular discs. The axis of the cylinder is defined as the line that runs from the center or connects […]

### At one point in a pipeline the water’s speed is 3.00 m/s and the gauge pressure is 5.00 x 10^4 Pa. Find the gauge pressure at a second point in the line, 11.0 m lower than the first, if the pipe diameter at the second point is twice that at the first.

The main objective of this question is to find the gauge pressure at the second point in the pipeline using Bernoulli’s equation. The continuity equation states that the product of the pipe’s cross-sectional area and fluid speed at any instant along the pipe must be constant. This product is equal to the flow rate or […]

### The three masses shown in the figure are connected by massless, rigid rods. Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page. Express your answer to two significant figures and include the appropriate units. Find the moment of inertia about an axis that passes through masses B and C. Express your answer to two significant figures and include the appropriate units.

This question aims to find the moment of inertia about the given axis of rotation. Inertia is a property of a body that opposes any force which attempts to move it or to change the magnitude or direction of its velocity if it is in motion. Inertia is a non-resistant property that allows a body to oppose active factors such as forces […]

### An object moving in the xy-plane is acted on by a conservative force described by the potential-energy function U(x,y) where ‘a’ is a positive constant. Derive an expression for the force f⃗ expressed in terms of the unit vectors i^ and j^.

[ U(x, y) = a Big( dfrac{1} {x^2} + dfrac{1} {y^2} Big) ] This question aims to find an expression for the Force f which is expressed in terms of the unit vectors i^ and j^. The concepts needed for this question include potential energy function, conservative forces, and unit vectors. Potential Energy Function is a […]

### A spring with Spring Constant k=340N/m is used to Weigh a 6.7-kg fish

This question aims to find the change in the length of spring (used to weigh 6.7-kg fish), which is displaced from its mean position. The value of the spring constant is given as k=340N/m. Hooke’s law states that the force exerted by the spring when stretched or compressed from its mean position is directly proportional […]

### When a honeybee flies through the air, it develops a charge of +16pC.

Calculate the number of electrons the honeybee loses while it develops the given charge while it flies. The aim of this article is to find the number of electrons being lost by the honeybee while it acquires a positive charge of +16pC as it flies through the air. The basic concept behind this article is the […]

### Did the electron move into a region of higher potential or lower potential?

When an electron with an initial speed of $6.00 times 10^5$ m/s, due to an electric field is brought to rest. Find a region i.e., either a higher potential or lower potential that the electron will move. Find the potential difference that is required to stop the electron. Find the initial kinetic energy […]

### In an experiment in space, one proton is fixed and other is released from rest (point A), from a distance of 5 mm away. What is the initial acceleration of the proton after it is released?

This question aims to find the initial acceleration of the proton released from a rest point A 5 mm away. The question is based on the concepts of Coulomb’s Law. Coulomb’s law is defined as the electric force between two point charges while they are at rest is called the coulomb’s law. The formula for […]

### Calculate the magnitude of the linear momentum for the following cases:

A proton with mass 1.67X10^(-27) kg, moving with a speed 5X10^(6) m/s. A 15.0g bullet moving with a speed of 300m/s. A 75.0 kg sprinter running with a speed of 10.0 m/s. Earth (mass = 5.98X10^(24) kg) moving with an orbital speed equal to 2.98X10^(4) m/s. The aim of this question is to learn the […]

### A force acting on a particle moving in the xy plane is given by F=(2yi+x^2 j)N, where x and y are in meters.

The particle moves from the origin O to a final position with the coordinates as x=4.65m and y=4.65m, which is also represented in the following figure. Figure 1 Find work done by F along OAC Find work done by F along OBC Find work done by F along OC Is F conservative or non-conservative? This […]

### What are the dimensions of the lightest open-top right circular cylinder can hold a volume of 1000 cm^3 ?

The main objective of this question is to find the dimension of the open cylinder which has a volume of 1000 cm^3. This question uses the concept of the volume and surface area for the circular cylinder which is open-top or close-top. Mathematically, the volume of a circular cylinder is represented as: [Vspace = space […]

### A proton with an initial speed of 650,000 m/s is brought to rest by an electric field.

Is the proton moving towards lower potential or higher potential? At what potential difference had the proton been stopped? How much kinetic energy (in electron-volts) did the proton carry at the start of the journey? The aim of this question is to understand the interaction of charged bodies with electric fields in terms of kinetic […]

### A uniform steel bar swings from a pivot at one end with a period of 1.2 s. How long is the bar?

The main objective of this question is to find the length of the steel bar. This question uses the concept of the pendulum. A pendulum is simply the weight suspended from a pivot or shaft so that it will move freely. The period of the pendulum is mathematically equal to: [Tspace = space 2 pi […]

### Determine the magnitude of the current in the (a) 8.0-ω and (b) 2.0-ω resistors in the drawing.

The main objective of this question is to find the direction and magnitude of the current in 0.2 ohm and 0.8 ohm resistors. This question uses the concept of Kirchoff’s current law and Kirchhoff’s voltage law to find the direction and magnitude of current for the given circuit diagram. In Kirchoff’s current law, the current […]

### A 2.0 kg piece of wood slides on the surface. The curved sides are perfectly smooth, but the rough horizontal bottom is 30 m long and has a kinetic friction coefficient of 0.20 with the wood. The piece of wood starts from rest 4.0 m above the rough bottom. Where will this wood eventually come to rest?

From the initial release until the wood reaches the state of rest, what amount of work is done by friction? This problem aims to familiarize with the concepts of dynamic motion which are part of classical dynamic physics. To better understand this topic you should be familiar with kinetic energy, kinetic friction, […]

### The current in a 50 mH inductor is known to be

i  = 120 mA, t<= 0  [ boldsymbol{ i(t) = A_1e^{ -500t } + A_2e^{ -2000t } A, t ge 0 } ] The potential difference across inductor terminals is 3V […]

### A +9 nC charge is located at the origin. What is the strength of the electric field at the position (x,y)=(−5.0 cm,−5.0 cm)

The purpose of this article is to learn the interaction between an electric charge and an electric field. We simply need to find the forces acting on the charged body under the influence of the electric field. To solve this question, we need to understand the mathematical forms of electric field and the force acting […]

### Two large parallel conducting plates carrying opposite charges of equal magnitude are separated by 2.20cm.

Calculate the absolute magnitude of Electric Field E in the area between the two conducting plates if the magnitude of charge density at the surface of each place is 47.0 nC/m^2. Calculate the Potential Difference V that exists between the two conducting plates. Calculate the impact on the magnitude of Electric Field E and Potential […]

### Unpolarized light with intensity I₀ is incident on two polarizing filters. Find intensity of the light after passing through second filter.

The first filter is oriented at an angle of $60.0°$ between its axis and vertical whereas the second filter is oriented at the horizontal axis. The aim of this question is to find the intensity of polarized light after it has passed through two filters which are oriented at a certain angle and axis. The […]

### A cart is driven by a large propeller or fan, which can accelerate or decelerate the cart. The cart starts out at the position x=0m, with an initial velocity of +5m/s and a constant acceleration due to the fan. The direction to the right is positive. The cart reaches a maximum position of x=12.5m, where it begins to travel in the negative direction. Find the acceleration of the cart.

The question aims to find the acceleration of the cart with initial speed vo=5 m.s^(-1). The term acceleration is defined as the rate of change of an object’s velocity with respect to time. Accelerations are normally vector quantities (in that they have magnitude and direction). The orientation of an object’s acceleration is represented by the orientation of the net […]

### What is the speed vgas of the exhaust gas relative to the rocket?

A rocket is fired in deep space, where gravity is negligible. In the first second, the rocket ejects $dfrac{1}{160}$ of its mass as exhaust gas and has an acceleration of $16.0$ $dfrac{m^2}{s}$. What is the speed of exhaust gas relative to the rocket? Rockets use propulsion and acceleration to lift off from the ground. Rocket […]

### A canoe has a velocity of 0.40 m/s southeast relative to the earth. The canoe is on a river that is flowing 0.50 m/s east relative to the earth. Find the velocity (magnitude and direction) of the canoe relative to the river.

This question aims to find the direction and magnitude of the velocity of the canoe with respect to the river.This question uses the concept of velocity. The velocity of an object has both direction and magnitude.  If the object is moving towards the right, then the direction of velocity is also towards the right. Expert […]

### A marble moves along the x-axis. The potential-energy function is shown in the figure (figure 1) .

At which of the labeled $x-$coordinates is the force on the marble zero? Which of the labeled $x-$coordinates is a position of stable equilibrium? Which of the labeled $x-$coordinates is a position of unstable equilibrium? The objective of this question is to identify the points at which the force on the marble is zero and […]

### What minimum energy is required to excite a vibration in HCl?

What wavelength of light is required to excite this vibration? The vibration frequency of HCI is $v= 8.85 times 10^{13} space s^{-1}$. This problem aims to familiarize us with vibrating molecules and the energy they dissipate or absorb from their surroundings. This problem requires the core knowledge of chemistry along with molecules and their movements. Let’s […]

### The earth’s radius is 6.37×106 m; it rotates once every 24 hours.

Calculate the angular speed of the earth. Calculate the direction (positive or negative) of the angular velocity. Assume you are viewing from a point exactly above the north pole. Calculate the tangential speed of a point on the earth’s surface located on the equator. Calculate the tangential speed of a point on the earth’s surface […]

### An astronaut on a distant planet wants to determine its acceleration due to gravity. The astronaut throws a rock straight up with a velocity of + 15 m/s and measures a time of 20.0 s before the rock returns to his hand. What is the acceleration (magnitude and direction) due to gravity on this planet?

This problem aims to find the acceleration due to the gravity of an object on a distant planet. The concepts required to solve this problem are related to gravitational physics, which include Newton’s equations of gravitational motion. A motion under the influence of gravity directs to the vertical movement of an object whose motion is […]

### A spherical interplanetary probe of 0.5m diameter contains electronics that dissipates 150 W. If the probe surface has an emissivity of 0.8 and the probe does not receive radiation from other surfaces, as, for example, from the sun, what is its surface temperature?

This article aims to find the surface temperature. According to Stefan Boltzmann’s law, the amount of radiation emitted per unit time from region $A$ of a black body at absolute temperature represented by $T$ is directly proportional to the fourth power of temperature. [dfrac{u}{A}=sigma T^{4}] where $sigma$ is the Stefan constant $sigma=5.67 times 10^{-8} dfrac{W}{m^{2}. {K}^{4}}$ is derived from other […]

### Boxes A and B are in contact on a horizontal friction-less surface. Box A has mass 20 kg and box B has mass 5kg.A horizontal force of 250N is exerted on box A. What is the magnitude of the force that box A exerts on box B?

This problem aims to familiarize us with a friction-less motion between two masses as a single system. The concept required to solve this problem includes acceleration, newtons law of motion, and the law of conservation of momentum. In this particular problem, we require the help of newton’s second law, which is a quantitative definition of […]

### Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of shaft power. The free surface of the upper reservoir is 45 m higher than that of the lower reservoir. If the flow rate of water is measured to be 0.03 m^3/s, determine mechanical power that is converted to thermal energy during this process due to frictional effects.

The main objective of this question is to find the mechanical power converted to thermal energy during the given process. Mechanical energy is the energy that an object possesses as a result of its motion or position. Mechanical energy is classified into two types, that is potential energy and kinetic energy. The potential energy refers to […]