UP PGT Physics Mock Test - 3 - UPTET MCQ

Kinetic energy at highest point,

Explanation:(a) for a given Periphery the area of a circle is maximum. When a coil takes a circular shape, the magnetic flux linked with the coil increases, so the current induced in the coil will tend to decrease the flux and so it will produce a magnetic field upward. As a result the current induced in the coil will flow in anticlockwise direction.(b) When circular coil takes the shape of narrow straight wire, The magnetic flux linked with the coil decreases. So the current induced in the coil will tend to oppose the decrease in magnetic flux. Hence it will produce an upward magnetic field so that the current induced in the coil will flow in anticlockwise direction.

Gravitational force between two objects is mathematically represented as:
F = G × (m₁×m₂) / r²
Applying the Law of Gravitation,
Given that the initial force F is due to two objects each of mass m separated by a distance r.
Substituting these into the formula gives:
F = G × (m×m) / r²
The problem then states that the mass of each of the objects is doubled (to 2m) and the distance between them is also doubled (to 2r).
The new force F' using these values in the formula would be: F' = G × (2m×2m) / (2r)²

Simplifying this gives:
F' = 4G × (m×m) / 4×r²
This simplifies further to:
F' = G × (m×m) / r²
Comparing this with the original equation for F, we find that:
F' = F

When Rutherford saw the results of the experiment by Geiger and Marsden, he said:
“It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”
Rutherford used the results of this experiment to develop a new model for the atom. This model proposed a central nucleus with a positive charge. It was this positively charged nucleus that was responsible for the strong backward deflection of the positively charged alpha particles.
The model also proposed that negatively charged electrons surrounded this nucleus. However, as most of the alpha particles passed through the gold foil with no deflection at all, Rutherford realised that most of the atom was empty space. So, his model placed the electrons at some distance from the nucleus.
 

Using formula for Paschen series,
1/λ=R[(1/3²)-1/n₂²],n₂=4,5,6….
For shortest wavelength, n₂=∞
∴1/λ=R[(1/3²)-1/∞²],n₂=R/9 or λ=9/R ≈ 820.4 nm

The impending motion refers to the state of a body when it is on the verge of slipping. In such cases, the static friction has reached its upper limit and is given by the equation, F=μ_sN

Explanation

To determine the number of significant digits in the number 8.1000, we can follow a systematic approach based on the established rules of significant figures

1Identify non-zero digits. In the number 8.1000, the digits '8' and '1' are non-zero. According to the rules of significant figures, all non-zero digits are considered significant. Therefore, we have two significant digits from these numbers

2Examine the zeros. The zeros in the number 8.1000 need to be evaluated based on their position. The first zero appears after the '1', and since it is sandwiched between non-zero digits (1 and 0), it is significant

3Analyze trailing zeros. The last three zeros in 8.1000 come after the decimal point and follow the last non-zero digit (which is '1'). According to the rules, trailing zeros in a decimal number are significant. Therefore, these three zeros also count as significant digits

4Count the total significant digits. Adding the significant digits identified: 2 (from '8' and '1') + 1 (from the zero between '1' and '0') + 3 (trailing zeros) gives us a total of 5 significant digits

In the case of a non-conducting sphere, an electric charge is uniformly distributed throughout the sphere. Inside the sphere, the electric field at a point will be only due to the electric charge inside that point. There will be no effect of the remaining charge outside that point. In the case of the conducting sphere, the electric field at every point inside the sphere is zero.

Hook’s Law states that for small deformations the stress and strain are proportional to each other.

From (i), (ii), and (iii)

Here negative sign signifies that the current is decreasing

From (v) and (vi)

On integrating

Substituting this value in (iv) we get

Let m be mass of each ball and q be charge on each ball. Force of repulsion,


In equilibrium
Tcosq = mg ...(i)
Tsinq = F ...(ii)
Divide (ii) by (i), we get,

From figure (a),



Divide (iv) by (iii), we get

The dimension of the units of a derived physical quantity may be defined as the number of times the fundamental units of mass, length and time appear in the physical quantity.

The expression for velocity obtained above is said to be its dimensional formula. Thus, the dimensional formula for velocity is [M⁰L¹T​​​​​​^-1].

Infrared waves are emitted by hot bodies. They are produced due to the de-excitation of atoms.
They are called Heat waves as they produce heat falling on matter. This is because water molecules present in most materials readily absorb infrared waves. After absorption, their thermal motion increases, that is, they heat up and heat their surroundings.
Uses: Infra red lamps; play an important role in maintaining warmth through greenhouse effect.

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.

• When a source of white light is used instead of a monochromatic source, the diffracted image of the slit gets dispersed into constituent colours of white light.
• The central maximum will be white and on either side of the central maximum, there will be coloured fringes.

v = v₀ ​+ gt + ft²
∫₀^x​ dx = ∫₀¹​(v₀​ + gt + ft²) dt
► x = v_{0 ​}+ g/2 ​+ f​/3

Because angular momentum remains constant as the moment of inertia is increasing here so the angular velocity will decrease.

Resultant force is zero, as three forces on the particle can be represented in magnitude and direction by three sides of a       triangle in same order. Hence, by Newton's 2nd law 

Particle velocity  will be same

t_1/2​=24000 yrs
It is stored for 3 half-lives.
Fraction remaining is (1/2​)³=1/8

As we know that the stopping potential of the photoelectron is equal to the maximum kinetic energy of the photoelectron,
KEmax​=10.4V
Now, in photoelectric effect,
Energy of incident radiation (E_in​) = work function + K.Emax​
⇒ E_in​=1.7+10.4
⇒ E_in​=12.1eV
Now, for 0 hydrogen atom,
Energy of first energy level, E₁​=−13.6eV
Energy of second energy level, E₂​=−3.4eV
Energy of third energy level, E₃​=−1.5eV
Hence, a transition from third to first energy level will result in emission of radiation of energy = E₃​−E₁​=12.1eV which is same as the energy of incident radiation of above photoelectric effect.
Thus, correct answer is n=3 to 1
 

I₀=250μA, v₀=3.6v .  v=1.6x10⁶ Hz
Here,
(Reactance of inductance) X_L=ωL
X_L=2πv X L
v₀/I₀=2πv x L
3.6/2.5x10^-4=2πx1.6x10^-6 x L
0.14x10^4-6=L
L=0.14x10^-2H
Now for v=16.0x10⁶Hz
XL=2πv X L
=2πx16x10⁶x14x10^-4
X_L=1407x10²Ω
Now,
v0=I0 x XL
3.6/1407x10²=I₀   [∵v0=kept constant.]
I₀=0.00256x10^-2
I₀=25.6μA

Here, current is uniformly distributed across the crosssection of the wire, therefore, current enclosed in the amperean path formed at a distance 

 where I is total current

∴ Magnetic field at P₁ is

Now, magnetic field at point P₂,

Force due to surface tension acts all along the circumference of the circular plate. Therefore, force required to take away of plate is,
F = T x 2πr = 70 x 2 x 3.14 x 4 = 1758.4 dyne/cm
 

Given Data,
Length of the piece of copper = l = 19.1 mm = 19.1 × 10^-3m
Breadth of the piece of copper = b = 15.2 mm = 15.2× 10^-3m
Tension force applied on the piece of cooper, F = 44500N
Area of rectangular cross section of copper piece,
Area = l× b
⇒ Area = (19.1 × 10-3m) × (15.2× 10-3m)
⇒ Area = 2.9 × 10^-4 m²
Modulus of elasticity of copper from standard list, η = 42× 10⁹ N/m2
By definition, Modulus of elasticity, η = stress/strain

⇒ Strain = F/Aη

⇒ Strain = 3.65 × 10^-3
Hence, the resulting strain is 3.65 × 10^-3

B=B₀+Bm
= μ₀nI+ μmnI
=nI(μ+ μm)
=60x5(5000μ₀+ μ₀)
B=300(5001μ₀)
B=1.88T
H=B/μm
=300x5001μ₀/5000μ
=300AT

For constant electric field

Explanation:

Threshold frequency: - frequency of minimum energy required to remove electron
 
work function=3.3ev
f=3.3×1.6×10⁻¹⁹J​ /6.626×10⁻³⁴J−s
=0.8×10¹⁵Hz
=8×10¹⁴Hz

The formula for calculating the escape velocity from the surface of a celestial body (e.g. a planet) is:

where G is the universal gravitation constant, M is the planet’s mass and R is its radius. Different planets have different mass and radius - and therefore different escape velocity.

Both statements are independently true but 2 is not the correct explanation of 1.
The reason for statement 1 is that while pulling, a component of force reduces the normal reaction and hence reduces the friction force.