UP PGT Physics Mock Test - 8 - UPTET MCQ

Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized.
So the angle of incidence would be 60°

By checking dimension all option
[Dipole moment] = [M⁰L¹T¹A¹] [Electric Flux] = [M¹L³T^-3I^-1] [Electric field] = [M¹L¹T^-3I^-1]

Magnetic field part of a harmonic electromagnetic wave in vacuum
,B₀​=510×10⁻⁹T
Speed of light,
C=3×10⁸m/s
E=cB_o​=153N/C

Same elastic properties in all direction is called the homogenity of a material.

Between two square faces the area is 0.01×0.01=1×10⁻⁴m² and length is 0.5m. So, the resistance is (3.5×10⁻⁵×0.5)/(1×10^-4)=0.175ohm, this can be written as, (35/2) x10^-2 ohm
Between the rectangular face the area is 0.01×0.5=0.005m² and the length is 0.01m, hence the resistance is (3.5×10⁻⁵×0.01)/0.005=7×10^-5 ohm

We know that,
X_L= ωL
Or, X_L =2πfL   [ ω can be written as, 2πf]
Initially,
X_L1=2πf₁L₁=1000Ω
For the second case,
F  and L both are doubled, so,
X_L2 =2π2f₁2L₁ =4x2πf₁L₁
                        =4000 Ω

L = Iw
L is the angular momentum, I is the MOI and w is the rotational velocity.
[I] = [ML²T⁰], [w] = [M⁰L⁰T^-1]
[L] = [MLT^-1]

g∝1​/R²
Curve b represents this variation.
 

As we know that, potential energy of a magnet in a magnetic field
U=−m⋅B
  =−mBcosθ
where, m= magnetic dipole moment of the magnet 
B= magnetic field

The only difference in covering any part of a lens is that the intensity of the image will reduce. Since the focal length is a function of curvature of the surfaces of the lens and covering a part does not change it, the image will be formed as usual.

According to Gauss’s principle, if there is no charge bound inside a surface, net electric flux coming out of the surface will always be 0. In this case, the charge is kept outside the surface, so it will generate no field lines and hence no flux inside the surface. The situation will be the same if an electric dipole is placed inside a surface as the dipole has equal positive and negative charges; the total charge inside the surface becomes 0.

g = GM​/R² 
g at height h
g_h​ = GM/(R+H)²
h = R/2
g_h ​= GM/(R + R/2​)² ​= GM/((9/4) (R²)) ​= 4/9g
Decrease in the value of g
g − 4/9g = 5/9 g

Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called "speed", being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s) or as the SI base unit of (m⋅s⁻¹).

Fringe width = λD/d
where λ us wavelength
D is the distance between slits & screen
d is the distance between slits

At infinity, image of B will form at focus since it is at infinity. Image of A will be at A which can be calculated by mirror formula.
1/v​+(1/−u)​=(1/−f)
⟹v= fu /(f−u)​=−( fu/(u−f)​)
Image length = v−f=(fu/(u−f)​)−(f)

= f^2​/(u−f)
(We take the absolute values of the distances to calculate the rod length)

E =F/q = (KQ/r²)

There is a condition of weightlessness in a satellite.
Therefore, mg=0
Due to electrostatic force of repulsion between the balls, the string would become horizontal.
Therefore, angle between the string =180
 

Impedance(X_C)=1/ω_C
=1/ 2πfC
=1/2πx50x10x10^-6
=10⁶/1000π
X_C=10³/π=(1000/π) Ω

When Young's double-slit set up for interference is shifted from air to within water then the fringe width decreases because the refractive index of water is more than that of the air.
Originally the fringe width is given by:
β1​=λD/2d​
The new fringe width within water will be given by 
β2​= λD​/2nd
So, β2​= β1/n​​
Here, n is the refractive index of medium.
 

Line charge density = λ
Radius, r = R
Now,  λdl=dθ
For total charge enclosed by radius R, ₀∫^R Q = ₀∫^R λdl
Q_inc = λR
Now, ϕ = Q_inc/ε_o    {from Gauss law}
= λR/ε₀

Angular acceleration is defined as the rate at which an object's angular velocity changes over time. It is given by the formula:
Angular acceleration (α) = Change in angular velocity (Δω) / Change in time (Δt)

If series LCR circuit is present then z={R²+(xl-xc)²}^1/2
if resonance is present then X_C=C_L or V_C=C_L then Z= Z_o
if LCR circuit is in parallel form then in which circuit resonance is also present firstly 1/Z ={(1/R)₂+ ((1/xc) –(1/xl))²}^1/2 and in resonance conditions X_C=C_L according to this Z= Z_o then option C is the correct answer

Phase Difference between Current and EMF in an Inductance
 

• Explanation: In an inductance, the current lags behind the electromotive force (EMF) by a phase angle of π/2 (90 degrees).


• Reasoning: This phase difference occurs because when the current starts to flow through the inductance, it induces a back EMF that opposes the change in current. This back EMF leads to the current lagging behind the EMF.


• Mathematically: The relationship between the current (I) and the EMF (E) in an inductance can be expressed as: E = L(di/dt), where L is the inductance and di/dt is the rate of change of current with respect to time. This equation shows that the EMF is proportional to the rate of change of current, leading to the phase difference.


 

mass = 50 x 100 = 5000 kg, g = 10 m/s²,  h = 10 m
Potential energy gained = mgh = 5000 x 10 x 10 = 5 x 10⁵ J

When the charge is given to inner cylinder than there is an electric field is produced between cylinders which is given by
and due to this a potential difference is developed between two cylinders.

Explanation:In order to take a safe turn, the cyclist has to bend a little from his vertical position. In this case, a component of the reaction provides the required centripetal force.If q is angle made by the cyclist with the vertical then

In actual practice, the value of q is slightly less because the force of friction also contributes towards the centripetal force.

On smooth inclined plane:
Acceleration of the body = g sin θ If s be the distance travelled, then

By law of conservation of angular momentum, in the absence of external torque angular momentum is conserved.
For angular momentum to be constant
τ = 0
Central force: zero torque

Percentage error of A