BITSAT Physics Test - 8 - JEE MCQ

Let the two points be A and B.
Applying Bernoulli's equation on both the points:

Let the displacement of the rod be x.
Therefore, 

Therefore, the restoring torque will be

Frequency of the oscillation:

This is our required solution.

Speed of the transverse wave is given by:

where T is the tension in the wire and µ is mass per unit length of the wire
Therefore,
T = µv²
Strain:

This is our required solution.

We know that
Tension in the string ∝ strain
Let the extension in the string in the second case is 'x'.
So,

This is the required solution.

We know that:
τ = RC
Therefore,

Therefore,
τ_A < τ_B < τ_C
Hence, it is the correct option.

Drawing the FBD of the blocks, we get:

Since the system is at rest, So
T₁ = mg
T₂ = T₁ = mg
T₂ = 2 x 10 = 20 N
Therefore, stress σ in the wire is given by:

Energy stored per unit volume is gievn by:

This is our required solution.

As the collision between the block A and block B is perfectly elastic and masses are same, velocities will be interchanged.
The velocity of the block B will be 2 m/s.
At the maximum compression, both blocks B and C will move with same velocity.
Using conservation of momentum

Using conservation of energy,
Kinetic energy of blocks (B + C) + Elastic potential energy of the spring = Initial kinetic energy of the block B

This is our required solution.

The equation of the standing wave is given by:

And the amplitude of the particle at a distance x from the fixed end is given by
A = 2a sin (kx)
Since the string is vibrating in second harmonics, so there will be two loops in the string.
Therefore,

Amplitude at the anti-node = 4 mm
Therefore, 2a = 4 mm
Thus, amplitude of particle 
This is our required solution.

Let the volume taken = V m³
Therefore, thermal capacity of calorimeter = V cal/g^oC
Mass of water = V x 1 = V m³
Mass of alcohol = V x 0.8 = 0.8 m³ 
Rate of cooling of water

Rate of cooling of alcohol

Since, the rate of cooling for both water and alcohol is same.
Therefore,

This is our required solution.

On approaching the nucleus, the kinetic energy of the α- particle will convert into potential energy.
Therefore, Decrease in kinetic energy = Increase in potential energy
Or,

This is our required solution.

Let the particles collide at a point with position vector 
So for collision, the two particles must be at that point at same time.
Thus,

Given that:

The relation between the momentum and the kinetic energy is given by:

But as K.E is same

If two unequal masses possess the same kinetic energy, then the heavier mass has greater momentum.

Given, Amplitude of the wave = A
Maximum velocity of particle V_max = 4v
(where v is the velocity of wave)
Maximum velocity of wave, v_max = 4v
or, v_max = Aω = 4v
∴ ω = 4V/A
Wavelength of the wave,

Imagine the total hole filled with matter so as to produce uniform sphere of radius R and density ρ. The filled hole can then be represented by point 
The remained of sphere of mass   The centre of mass of these two-part must be at centre of the mass of the sphere

A galvanometer can be converted into a voltmeter by connecting a high resistance in series with the galvanometer. Let V be the potential difference to be measured by galvanometer. To do so, a resistance R of such a value is connected in series with the galvanometer so that if a potential difference V is applied across the terminals A and B, a current I_g flows through the galvanometer.
Now, total resistance of voltmeter = G + R From Ohm's law, 

Here, The current through the galvanometer

To reduce the deflection from 30 divisions to 20 divisions, the required current

The required resistance R is given by

Width of diffraction pattern, 

The width of the diffraction pattern is y/3

The dimension of Planck's constant is similar to angular momentum.
It is a physical constant that is the quantum of electromagnetic action. It relates the energy carried by a photon to its frequency by, E = hv

Where, E = energy, v = frequency and h = Planck's constant.
Now,
Dimensional formula of energy (E) = (ML²T^-2)
(Dimensional formula of frequency (v) = (T^-1]
The dimension of the Planck's constant is (h)

Angular momentum:
It is the rotational equivalent of linear momentum.
⇒ L = r × p
Where, L = angular momentum, r = distance and p = linear momentum.
Now,
Dimensional formula of (r) = (L)
Dimensional formula of (p) = [MLT^-1]
Therefore, the dimensional formula of L is

The efficiency of a heat engine is defined as the ratio of work done to the heat supplied, i.e., 


where T₂ is temperature of sink, and T₁ is temperature of hot reservoir. 

It is given that, m = 10 kg , v₁ = 20 m / sec, v₂ = 30 m / sec, and dt = 0.6 sec
We know thta, the momentum is given by,
⇒ P = mv ---- (1)
So initial momentum is given by,

And final momentum is given by,

By equation (2) and equation (3), the change in momentum is given by,

We know that the impulse is equal to the change in momentum,

Given that the current in primary coil of transformer is, i_p = 4A
Number of turns in primary coil of transformer is, N_p = 140
Number of turns in secondary coil of transformer is, N_s = 280
As we know that the ratio of the number of turns in a transformer is̤:

The passenger tends to lean forward when a running metro stops suddenly. It is because of Inertia of Motion.

We know that,
Newton’s First Law: A body continues to be in its state of rest or of uniform motion along a straight line unless it is acted upon by some external force to change the state. If no net force acts on a body, then the velocity of the body cannot change i.e., the body cannot accelerate. Newton’s first law defines inertia and is rightly called the law of inertia.

The inertia of motion is the inability of a body to change by itself its state of uniform motion i.e., a body in uniform motion can neither accelerate nor retard on its own.

When the running metro stops suddenly, the passenger tends to lean forward because the lower part of his body comes to rest with the ground but the upper part tends to continue its motion due to inertia of motion.

Given, initial time period of the simple pendulum, T₁ = T
Initial length of the pendulum,L₁
Let final length of the pendulum, L₂
L₂ = 1.21 L₁
Time period of Simple pendulum,

Current sensitivity of M₁

Current sensitivity of M₂

Ratio of the current senstivites of two moving coil galvanometers M₁ and M₂ is,

In the steady state, no current flows through the branch containing the capacitor. So, the equivalent circuit will be of the form as shown below :

The effective resistance of the circuit is

The current through the ciruit is

Let current i₁ flows through 2Ω resistance.

If p-n junction is unbiased then the current is zero because the drifting of charge is the same from both sides. As the concentration of electrons is less in the P-side compared to the n - side the electrons will diffusion n to the P-side of the junction.
In the case of holes, it occurs in vice versa for holes, this diffusion of electrons from n to P constitutes diffusion current from P to n. As a consequence of this diffusion there creates a region that is depleted from charges known as the depletion region.
The barrier potential set up across the junction produces a current from n to P which is known as drift current which is in opposite direction to the diffusion current.

When a magnet is brought near a conducting loop along its axis, the distance between the loop and the magnet will reduce so the intensity of the magnetic field associated with the loop also increases.
Because the magnetic field associated with the loop increases so the magnetic flux linked with the loop also increases.
So in this case the magnetic flux is changing, hence an electric current will generate.  
From the above equation, it is cleared that the induced emf depends upon the magnetic field and number of turns and it is independent of the resistance of the coil.

In an adiabatic process.

Thus, from Eq. (i), we have:

Given, equation of standing wave is:
y = a sin(100 t). cos(0.01 x)
We know that the standard equation of standing wave is:
y = a sin(ωt).cos(kx)
Comparing the given equation with standard equation, we get
ω = 100 and k = 0.01
Velocity of standing wave,

Given:
The radius of the tirst bohr orbit = a₀ according to 3rd Postulate of bohr atomic model 

and n corresponds to a permitted value of orbit radius. According to newtons second Law :a radially inward centripetal force,