Physics Test 244

Explanation:

Temperature: The temperature will vary along the length of the cylinder because the ends are maintained at different temperatures.

This creates a temperature gradient.

Density: The density of the gas may also vary along the length of the cylinder because temperature affects the density.

A higher temperature can cause the gas to expand, reducing its density, and vice versa.

Pressure: In a cylinder containing gas, if it is in a steady state and no external forces (like gravity) are acting on it, the pressure typically remains constant throughout the cylinder.

This is because any pressure difference would cause the gas to move and equalize the pressure throughout the system.

Molar concentration: This might change with temperature, as temperature can affect how the molecules are distributed in the gas.

∴ The correct option is 1

 Calculation:

For a point charge q located at a distance r from the charge, the electric potential 

V is given by:

V= kq/r​

Electric Potential

V = (qK / 2× 10^-2) - (qK / 8× 10^-2)

V = (3/8) 10²qK

∴ The correct option is 1)

• When a trivalent impurity (an element with three valence electrons, such as boron) is added to a pure semiconductor (like silicon), it results in the formation of "holes" in the crystal structure.
• Trivalent atoms have one less electron than needed to complete the bonding with neighboring silicon atoms.
• This missing electron creates a "hole," which acts as a positive charge carrier in the material. Thus, the addition of a trivalent impurity leads to a p-type semiconductor with holes as the majority charge carriers.
  
  Additional Information 
   
• The process of adding impurities is called doping.
• An extrinsic semiconductor is of 2 types: n-type and p-type.
• When the trivalent impurity is added to an intrinsic or pure semiconductor (silicon or germanium), then it is said to be a p-type semiconductor.
• Trivalent impurities such as Boron (B), Gallium (G), Indium (In), Aluminum (Al), etc are called acceptor impurity.
• When a pentavalent impurity is added to an intrinsic or pure semiconductor (silicon or germanium), then it is said to be an n-type semiconductor.
• Pentavalent impurities such as phosphorus (P), arsenic (As), antimony (Sb), etc are called donor impurity.

Explanation:

It is given that the satellite and the meteorite collide completely in-elastically. Hence its momentum will be conserved but its kinetic energy will not be conserved and will move together as a single body. The collision of the meteorite and the satellite should be taken at an angle of 90, since the satellite is moving in a circular orbit and the meteorite is moving towards the earth.

Let us consider the Initial Momentum of the satellite and the meteorite to be P = Mv

where M is the mass of the meteorite as well as the satellite and v is the orbital velocity through which the satellite revolves around the earth and is the same for the meteorite too.

In the above diagram, P₁ is the momentum of the satellite orbiting the earth and P₂ is the momentum of the meteorite moving towards the earth. Their resultant is given by P by the laws of vector addition.

Using the law of conservation of momentum,

Initially, the satellite was orbiting around the earth with an orbital velocity of v but when the collision happened the meteorite and the satellite started moving with velocity, V = 0.707v, which signifies that the velocity decreased.  

Since the Velocity after the collision is less than of orbital velocity. Hence it does not follow a circular path and travels in an elliptical orbit.

CONCEPT:

Simple harmonic motion:

• Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position.
  • The direction of this restoring force is always towards the mean position.

Natural frequency

• It is the frequency at which a system tends to oscillate in the absence of any driving or damping force.

​CALCULATION:

EXPLANATION:

→Bi-Metalic strip: The word 'Bi' means two. When two metal strips of different materials but equal lengths are joined together it is called a 'Bi-Metalic strip'.

→As the two metals are made of different materials they have different coefficients of linear expansion. 

So, on heating the metal with greater coefficients of linear expansion will expand more. 

→According to the question, α_AI > α_steel. ∴ Aluminum will expand more on heating. 

So, Aluminium will bend more and will be on the convex side.

→The metal with smaller α i.e steel will bend less and will be on the concave side. 

So, the correct answer is option (4).

The correct answer is option 4) i.e. 7 : 2

CONCEPT:

• Rotational kinetic energy: Rotational kinetic energy is due to the motion of an object's rotation.

For a given fixed axis of rotation, the rotational kinetic energy is given by:

Where I is the moment of inertia, ω is the angular velocity.

• Moment of inertia of a sphere about its central axis:
  • ​​​For a sphere of mass M and radius R, the moment of inertia (I_C) about an axis passing through its centre is given by