UP PGT Physics Mock Test - 3 - UPTET MCQ

Gravitational force between two objects is mathematically represented as:
F = G * (m1*m2) / r²
Applying the Law of Gravitation to the Given Problem
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

Thus, the force remains the same (F) even when the mass of each of the objects is doubled and the distance between them is also doubled. Hence, the correct answer is A: F.

The acceleration due to gravity on surface of earth is
g=GM​/ R²
 
g=GρV​/R²
where, G is the gravitational constant, M  is mass of earth, R  is radius of earth, ρ is the density and V is the volume of earth.
∴g=Gρ(4/3)​πR^3​/ R²
 
∴g=(4/3)​GρπR
⇒g∝ρR
since, all other quantities are constant.
Hence, if the radius of the earth be increased by a factor of 5, density will decrease by 5  to keep the value of g the same.

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

Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutrons bound together into a particle identical to a helium-4 nucleus. They are generally produced in the process of alpha decay, but may also be produced in other ways.

• The horsepower (hp) is a unit in the foot-pound-second ( fps ) or English system, sometimes used to express the rate at which mechanical energy is expended.
• It was originally defined as 550 foot-pounds per second (ft-lb/s).
• A power level of 1 hp is approximately equivalent to 746 watt.

The relative permeability of ferromagnetic materials is much larger than 1. Ferromagnetic substances are those, which when placed in a magnetic field are strongly magnetized in the direction of the magnetizing field, i.e., it is strongly attracted by a magnet.

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.

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.

The dimensional formula of a given unit is [ML²T⁻³A⁻²].
So, from the given option only resistance has this dimensional formula so resistance is the correct answer.

Applying Bernoulli's principle, we have
P₁+1/2​ρv₁²=P₂+1/2​ρv₂² 
⇒P₂​−P₁=1/2ρ (v2/1−v2/2)
⇒ΔP=1/2​×1.3× (1202−90²)
⇒ΔP=0.65× (120+90) × (120−90)
⇒ΔP=0.65×210×30=4095Pa

An oscillator is a circuit which produces a continuous, repeated, alternating waveform without any input. Oscillators basically convert unidirectional current flow from a DC source into an alternating waveform which is of the desired frequency, as decided by its circuit components.

Let, the length of wire = l unit

Fraction required =a

Then, the lenght of wire which is stretched =al

The Critical Angle
a light ray is in the more dense medium and approaching the less dense medium.
The angle of incidence for the light ray is greater than the so-called critical angle.
When the angle of incidence in water reaches a certain critical value, the refracted ray lies along the boundary, having an angle of refraction of 90-degrees. This angle of incidence is known as the critical angle; it is the largest angle of incidence for which refraction can still occur. For any angle of incidence greater than the critical angle, light will undergo total internal reflection.

The resolving power of a telescope is given by RP∝2μsinθ​/122λ
Further, sinθ ∝ tanθ ∝ diameter of the objective.
So, the resolving power of a telescope depends on the diameter of the objective lens.

Heat extracted from source Q1= 700 cal
Heat rejected to the sink Q2= 500 cal
Temperature of source T1= 150 +273= 423K
Temperature of sink T2 to be found:
 Q2/Q1 = T2/T1
So,
T2 = (Q2/Q1) x T1
= (500 x 423)/700
= 302.02 K
= 29.02 degree C.
 

Time constant is a measure of delay in an electrical circut resulting from either an inductor and resistor or capacitor and resistor. I will discuss rhe most common case which is resistor and capacitor, however the inductor resistor combination behaves in a similar manner. The time constant is equal to the value of the resistance in ohms multiplied by the value of capacitance in Farads. The time constant is measured in seconds . It represents the time for the voltage to decay to 1/2.72.

The SI base units and their physical quantities are the metre for measurement of length, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for temperature, the candela for luminous intensity, and the mole for amount of substance.

Only electron microscope has resolution of 0.5-0.6 Angstrom which is less than the size of an atom.

Total emf = 3 x 4 = 12 V
Total resistance = 6 + 3r
Current in the circuit = 2 A
Using ohm's law
2 = 12/ (6+3r)
2(6+3r)=12
12+6r=12
6r = 12-12 = 0
r = 0/6 = 0

The magnetic moment of a current carrying loop is given by

the direction is towards positive z-axis.

For the right (half) oscillation,

For the left (half) oscillation,

Let particle (1) is moving towards right and particle (2) is moving towards left art this instant, 1 = 0 

∆ U = ∆ Q - ∆ W
In an adiabatic process ∆Q is zero, therefore
∆ U = - ∆ W

Correct Answer :- d

Explanation : μ_total = MV

= (8*10⁵)(2*10^-2)

= 6A m²

Magnetic field on the axis of a current loop with magnetic material μtotal is:

B = μ₀ μ_total / (2π(x² + a²)^1/2

B = (4π*10^-7)(6) / [2π(0.1)]

= 1 * 10^-3 T

= 0.001 T

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.

Explanation:

e = Rate of change of magnetic field x area

From the formula we get,
X_L=X_C
ωL=1/ωC
⇒ω²=1/LC
⇒ω=1/√Lc
⇒ω=1/√10^-3x10^-5
⇒ω=10⁴
We also know that,
X_L=ωL
⇒X_L=104x10-3
⇒X_L=10 Ω
Therefore,X_L=X_C=10Ω