Physics Test-3

Uniform motion is the kind of motion in which a body covers equal displacement in equal intervals of time. It does not matter how small the time intervals are, as long as the displacements covered are equal.

If a body is involved in rectilinear motion and the motion is uniform, then the acceleration of the body must be zero.

The energy of electron in the \(n ^{\text {th }}\) state of hydrogen atom is:

\(E_n=\frac{-13.6}{n^2}~ eV\)

The energy of electron in the ground state \(( n = 1)\) of hydrogen atom is \(-13.6~ eV\).

The energy required for the transition from \(n =2\) to \(n =3\) i.e., excitation energy required to excite an electron from state \(n =2\) to \(n =3\) is:

\(\Delta E =\frac{ -13.6}{ n _3^2}-\frac{ -13.6}{ n _2^2}\)

\(\Delta E =(-13.6)\left[\frac{1}{3^2}-\frac{1}{2^2}\right]\)

\(\Delta E =-13.6\left[\frac{-5}{36}\right]\)

\(\Delta E =1 . 89 ~eV\)

Electroplating prevents corrosion.

Electroplating gives metal protection from corrosion, as it is a process of coating the base metal with another metal. The base metal is inexpensive but the other metal used here is pure metal or one of several alloys.

According to the given reaction, we can write

\(\mathrm{E}=\mathrm{E}^{\circ}-\frac{0.059}{2} \log \frac{\left[\mathrm{Cu}^{2+}\right]}{\left[\mathrm{Ag}^{+}\right]^{2}}\)

The cell potential will increase the most by doubling the concentration of \(\mathrm{Ag}^{+}\) ion.

Biot-Savart Law: The law that gives the magnetic field generated by a constant electric current is Biot-savart law.

Let us take a current-carrying wire of current \(I\) and we need to find the magnetic field at a distance \(r\) from the wire then it is given by:

\(d B=\frac{\mu_{0} I}{4 \pi}\left(\frac{\overrightarrow{d l} \times \hat{r}}{r^{2}}\right)\)

Where, \(\mu_{0}=4 \pi \times 10^{-7}\) T.m/A is the permeability of free space/vacuum, \(dl =\) small element of wire and \(\hat{r}\) is the unit position vector of the point where we need to find the magnetic field.

From the above expression of the Biot-savart law, the magnetic field is:

• Directly proportional to the lengthof the wire. So statement (i)is correct.
• Directly proportional to the electric current. So statement (iii) is correct.
• Biot-savart law gives the magnetic field, not the electric field. So statement (ii) is wrong.

The direction of the angular velocity vector is perpendicular to the plane of rotation and follows the right-hand rule. When the rotation is counterclockwise, the angular velocity vector points upward.

The partially submerged body resembles the floating body, where the weight of the body is balanced by the buoyancy force acting in the upwards direction. The stability of the floating is governed by the metacentre of the floating body.

Metacentre is the point about which a body starts oscillating when the body is tilted by a small angle. It is the point where the line of action of buoyancy will meet the normal axis of the body when the body is given a small angular displacement.

An electrolyte isa liquid that conducts current.

An electrolyte is a substance that dissociates into ions in solution and acquires the capacity to conduct electricity. Sodium, potassium, chloride, calcium, and phosphate are examples of electrolytes, informally known as lytes. Therefore, it a liquid that conducts electricity.

If a rectangular loop carrying a steady current is placed in a uniform magnetic field then it will experience a torque.The net force on the loop will be zero.

The torque on the current-carrying rectangular loop is given as,

τ = NIAB sinθ

Where, N = number of turns in the coil, I = current in the loop, A = area enclosed by the loop, B = magnetic field intensity, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field.

When wire CD is made to slide on wires PQ and ST, the flux linked with the circuit changes with time and hence an emf is induced in the circuit, which is given by:

\(| e |=\frac{ d \phi}{ dt }=\frac{ d }{ dt }( BA )= B \frac{ dA }{ dt }\)

The induced current is: \(I=\frac{e}{R}=\frac{B w v}{R}\)

This current is caused by the motion of wire CD. From Lenz's law, the current I opposes the motion of wire \(C D\). Therefore, work has to be done to slide the wire CD. Now, the magnetic force on wire CD (of length \(w\) ) is

\(F = BIw = B \left(\frac{ Bw }{ R }\right) w =\frac{ B ^2 w ^2 v }{ R }\)

Work done is sliding wire \(C D\) through a small distance \(d x\) in time \(d t\) is

\(dW = Fdx\)

Therefore, the work done per second is

\(P =\frac{ dW }{ dt }= F \frac{ dx }{ dt }= Fv\)

Using equation (1), we get

\(P =\frac{ B ^2 w ^2 v ^2}{ R }\)

\(P = \frac{(B w v)^2}{R}\)