SRMJEEE Physics Mock Test - 3 - JEE MCQ

The control rod in a nuclear reactor is primarily made of materials that absorb neutrons to regulate the fission process.

• Cadmium is commonly used due to its effectiveness in neutron absorption.
• Other materials such as boron and silver may also be employed for similar purposes.
• Graphite and uranium, although used in reactors, are not suitable for control rods.

The nuclear reactor at Kaiga is primarily a power reactor. It is designed to generate electricity through nuclear fission. Key points include:

• Location: Kaiga, India.
• Type: It serves as a power generation facility.
• Function: Utilises nuclear fission to produce energy.

When two wires with different resistivities are connected in series, the total resistance can be determined as follows:

• The total resistance in a series circuit is the sum of the individual resistances.
• Each wire's resistance is influenced by its resistivity, given by the formula: R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area.
• Since the wires have the same dimensions, the total resistance can be expressed as:
• R_total = R₁ + R₂ = (ρ₁L/A) + (ρ₂L/A)
• This simplifies to R_total = (ρ₁ + ρ₂)(L/A).
• Thus, the equivalent resistivity of the combination is:
• ρ_equiv = (ρ₁ + ρ₂)

Drift velocity is influenced by the diameter of the wire and the potential difference applied. When the diameter is doubled, the following effects occur:

• The cross-sectional area of the wire increases, allowing more electrons to flow through.
• According to the drift velocity formula, it is inversely proportional to the area.
• If the diameter is doubled, this results in a fourfold increase in cross-sectional area.
• Thus, the drift velocity will become one fourth of its original value.

The de Broglie wavelength associated with a particle can be calculated using the formula:

• The wavelength is given by h divided by the product of the mass m and velocity v.
• This relationship shows that as the mass or velocity increases, the wavelength decreases.
• The formula can be summarised as: wavelength = h / (mv).

C = 1μF
V = 1KV
energy stored U = 1/2 (CV²)
= 1/2 * 1 * 1² = 0.5

When high voltage is cut off, touching the terminals of a capacitor can be dangerous.

• Capacitors can store energy even after power is removed.
• They have a tendency to discharge that stored energy.
• This discharge can lead to dangerous effects if not handled properly.

Always exercise caution when dealing with capacitors to avoid potential hazards.

It is easier to roll a barrel than pull it along the road.

Rolling a barrel is generally more efficient than pulling it for several reasons:

• Reduced Friction: Rolling reduces the contact area with the ground, leading to less friction.
• Weight Distribution: The weight of the barrel is better distributed when rolled, making it easier to move.
• Energy Efficiency: More energy is conserved when rolling compared to the effort required to pull.

In summary, rolling is a more practical method for moving a barrel than pulling it.

If the radius of the Earth contracts by 2% while its mass remains unchanged, the weight of a body at the Earth's surface will be affected.

• The weight of an object is influenced by the gravitational force, which depends on both the mass of the Earth and the distance from its centre.
• When the radius decreases, the distance from the Earth’s centre to the surface also decreases.
• According to the formula for gravitational force, a smaller radius increases the gravitational pull on objects at the surface.
• As a result, the weight of a body at the Earth's surface will increase.

To determine the energy radiated by a black body when its temperature changes, we can use the Stefan-Boltzmann law, which states that the power radiated by a black body is proportional to the fourth power of its absolute temperature.

• Convert the initial temperatures from Celsius to Kelvin:
  • 227°C = 500 K
  • 727°C = 1000 K
• Calculate the ratio of the temperatures:
  • Using the fourth power: (1000 K / 500 K)⁴ = 16
• Calculate the new energy radiated:
  • Initial energy: 20 J
  • New energy = 20 J × 16 = 320 J

The energy radiated at 727°C is therefore 320 J.

To determine the new pressure of the gas after its mass is doubled, we can apply the principles of gas laws.

• The initial pressure of the gas is 75 cm of Hg.
• When the mass of the gas is doubled, while keeping the temperature and volume constant, we look at the relationship between pressure, volume, and temperature.
• According to the ideal gas law, pressure is directly proportional to the number of moles (or mass) of the gas.
• Doubling the mass of the gas will also double the pressure.
• Thus, the new pressure can be calculated as follows:

New pressure = 2 x 75 cm of Hg = 150 cm of Hg.

Therefore, the new pressure of the gas after doubling its mass is 150 cm of Hg.

The magnetic field at the centre of a circular coil can be determined using the formula:

• B ∝ I / r for a coil of radius r.

For the first coil:

• Radius = r
• Field = B₁ = k * I / r (where k is a constant).

For the second coil:

• Radius = 2r
• Field = B₂ = k * I / 2r.

Now, we find the ratio of the two magnetic fields:

• B₁ / B₂ = (k * I / r) / (k * I / 2r)
• This simplifies to B₁ / B₂ = 2.

Thus, the ratio B₁ / B₂ is 2.

The retarding viscous force acting on a spherical ball falling in a viscous fluid is influenced by several factors:

• Viscous force is a force that opposes the motion of the ball.
• This force depends on the radius of the ball and the velocity at which it falls.
• As the radius increases, the force increases due to greater surface area.
• Conversely, as the velocity increases, the force does not increase proportionally, as it is influenced by the fluid's viscosity.
• Hence, the relationship is such that the viscous force is directly proportional to the radius but inversely proportional to the velocity.

Given two wires made of the same material, we can determine the increase in length when subjected to different forces and dimensions.

• The first wire has a length of L and radius a, and it stretches by l when a force F is applied.
• For the second wire, the parameters are doubled: it has a length of 2L and radius 2a, while the applied force is 2F.

To find the increase in length of the second wire, we use the relationship for elongation, which is proportional to the force applied and inversely proportional to the cross-sectional area and length of the wire.

• The cross-sectional area of the first wire is πa², while for the second wire, it is π(2a)² = 4πa².
• Using the formula for elongation: Δl = (F × L) / (A × Y), where Y is Young's modulus (constant for the same material), we can compare the two wires.
• For the first wire, the elongation is:
• l = (F × L) / (πa² × Y)
• For the second wire, substituting the new values:
• Δl = (2F × 2L) / (4πa² × Y) = (4FL) / (4πa²Y) = (F × L) / (πa²Y) = l

The increase in length of the second wire is therefore l.

To determine the maximum safe speed of a car on a banked circular road, we can follow these steps:

• Identify the key parameters:
  • Radius of the road: 1000 m
  • Banking angle: 45°
  • Mass of the car: 2000 kg
  • Coefficient of friction: 0.5
• Calculate the forces acting on the car:
  • The gravitational force acting downwards: mg
  • The normal force acting perpendicular to the surface of the road.
  • The frictional force acting parallel to the road surface.
• Determine the centripetal force required:
  • The formula for centripetal force is: F_c = mv²/r
• Combine the forces:
  • The centripetal force is provided by the horizontal component of the normal force and the frictional force.
  • Equation: F_c = N sin(θ) + f cos(θ)
• Substitute the values and solve:
  • With θ = 45°, calculate the contributions of normal and frictional forces.
  • After calculations, determine the maximum safe speed.

The calculated maximum safe speed will yield the final answer.

To find the initial velocity of the particle, follow these steps:

• The position functions are given as:
• x = 2t²
• y = t² - 4t
• z = 3t - 5
• Calculate the velocity components by differentiating each position function with respect to time (t):
• v_x = d(x)/dt = 4t
• v_y = d(y)/dt = 2t - 4
• v_z = d(z)/dt = 3
• Evaluate the velocity components at t = 0:
• v_x(0) = 4(0) = 0
• v_y(0) = 2(0) - 4 = -4
• v_z(0) = 3
• The initial velocity vector is:
• v = (0, -4, 3)
• To find the magnitude of the initial velocity:
• Magnitude = √(0² + (-4)² + 3²)
• Magnitude = √(0 + 16 + 9) = √25 = 5 units

The initial velocity of the particle is 5 units.

To determine the reading on the spring balance when the lift descends with an acceleration equal to the acceleration due to gravity 'g':

• The weight of the body is calculated using the formula: Weight = mass × gravity.
• For a mass of 2 kg, the weight is: 2 kg × g.
• When the lift accelerates downwards at 'g', the effective acceleration acting on the body becomes zero.
• As a result, the spring balance will show a reading of zero, indicating that the body is in free fall.

The reading on the spring balance is zero.

Hypermetropia is a vision condition where distant objects can be seen clearly, but close ones appear blurry. This condition is often referred to as:

• Long-sightedness - Individuals struggle to focus on nearby items.
• Common causes include the shape of the eye or aging.
• People with hypermetropia may experience eye strain or headaches.

Corrective measures can involve:

• Prescription glasses or contact lenses.
• In some cases, surgical options may be considered.

To find the velocity of a body in simple harmonic motion, you can use the following formula:

• Angular frequency (ω) = 2 rad/s
• Amplitude (A) = 60 mm
• Displacement (x) = 20 mm

The velocity (v) at a given displacement can be calculated using the formula:

• v = ω * √(A² - x²)

Substituting the known values:

• v = 2 * √(60² - 20²)
• v = 2 * √(3600 - 400)
• v = 2 * √3200
• v = 2 * 56.57
• v ≈ 113.14 mm/s

Therefore, the velocity of the body at 20 mm displacement is approximately 113 mm/s.

To determine the energy stored in a spring when it is extended:

• The energy stored in a spring can be expressed in terms of the tension (T) and the spring constant (k).
• When a spring extends by a distance x, the relationship between tension, spring constant, and extension is relevant.
• The formula for the energy stored in a spring is derived from the work done in stretching it, which can be expressed as:
• Potential Energy = (T^2) / (2k)
• This indicates that the energy stored is directly related to the square of the tension divided by twice the spring constant.

To determine the angle θ at which two plane mirrors can render a reflected ray parallel to its original direction, consider the following points:

• When a ray strikes the first mirror, it reflects off at the same angle to the normal.
• After reflecting from the second mirror, the ray must remain parallel to its original path.
• This condition is satisfied when the total angle of reflection equals 180 degrees.
• The relationship between the angle of inclination θ of the mirrors and the angles of incidence and reflection leads to:
• 2θ = 180 degrees, which simplifies to θ = 90 degrees.

Thus, the angle θ required is 90 degrees.

The angular speed of a flywheel making 120 rpm is calculated as follows:

• First, convert the revolutions per minute (rpm) to revolutions per second (rps):
  • 120 rpm ÷ 60 seconds = 2 rps
• Next, convert revolutions to radians:
  • 1 revolution = 2π radians
• Now, calculate the angular speed in radians per second:
  • Angular speed = 2 rps × 2π radians = 4π radians/s

Therefore, the angular speed of the flywheel is 4π radians/s.

The kinetic energy of a rotating ring can be calculated using the following principles:

• The formula for the moment of inertia (I) of a ring about an axis through its centre is given by I = mr².
• The kinetic energy (KE) of a rotating object is determined by the formula KE = 0.5 * I * ω².
• Substituting the moment of inertia into the kinetic energy formula, we have:
• KE = 0.5 * (mr²) * ω².
• This simplifies to KE = (mr²ω²) / 2.

The final expression for the kinetic energy of the rotating ring is therefore mr²ω²/2.

When electric bulbs are connected in series, the same current flows through each bulb.

• The current is determined by the total resistance in the circuit.
• In a series connection, all components share the same current.
• The power ratings (60 W and 100 W) indicate how much energy they consume, not the current they carry.

Therefore, the current passing through both bulbs is the same.

When the heat energy is supplied to the liquid, it is absorbed by the liquid and a phase change occurs from liquid state to gaseous state. The amount of heat absorbed by the liquid molecules is transferred to the vapor molecules.
Thus latent heat 'L' is given by,

L=Q/m​
 

where Q is the amount of heat energy supplied to the liquid and m is mass of the liquid.

For a unit mass of liquid,
 

L=Q
 

The latent heat of vaporization is the amount of heat energy supplied by heating, according to first law of thermodynamics,

L=δE+PδV
δE=L−PδV
δE=L−P(V2​−V1​)

where,
δE is change in internal energy of the gas,
P is atmospheric pressure,
δV is change in volume
V1 is the volume of liquid and
V2 is the volume of gas

When the distance between a light source and an observer decreases, the apparent frequency of light changes due to the Doppler effect.

The key points are:

• Apparent frequency refers to how the frequency of light is perceived by the observer.
• As the observer moves closer to the light source, the light waves are compressed.
• This compression results in an increase in the frequency of light.
• Consequently, the observer perceives the light to be of a higher frequency, which is seen as a shift towards the blue end of the spectrum.

To determine the ratio of wave velocities in wires A and B, we can use the formula for wave velocity in a stretched string:

• Velocity (v) is given by the formula: v = √(T/μ), where T is the tension and μ is the linear mass density.
• The linear mass density (μ) can be calculated as: μ = ρA, where ρ is the density and A is the cross-sectional area.
• For a wire, the area A is proportional to the square of the diameter. If wire A has a diameter twice that of wire B, then:
• A_A = 4A_B (since area is proportional to the square of the diameter).
• Using the tension values:
• T_A = ½ T_B.
• Now, we can express the linear mass densities:
• μ_A = ρ(4A_B) = 4ρA_B
• μ_B = ρA_B
• Substituting into the velocity formula:
• v_A = √(T_A / μ_A) = √[½ T_B / (4ρA_B)] = √[T_B / (8ρA_B)].
• v_B = √(T_B / μ_B) = √[T_B / (ρA_B)].
• Taking the ratio of the velocities:
• v_A / v_B = √[T_B / (8ρA_B)] / √[T_B / (ρA_B)] = √(1/8) = 1/√8 = 1/(2√2).

Therefore, the ratio of velocities in wires A and B is: 1 : 2√2.