৪৯তম বিসিএস ⎯ পদার্থবিদ্যা [৫১১]

In pure rolling motion, both translational and rotational kinetic energy contribute to the total kinetic energy. If no external force or torque is acting, linear momentum, angular momentum, and kinetic energy all remain conserved. However, in the presence of friction or external torques, conservation may break down. So, "none of these" is correct because all three can be conserved under ideal pure rolling conditions.

Source: [HSC Physics book & H.C. Verma Vol I – Chapter: Rotational Mechanics]

In physics, many concepts in rotational motion have counterparts (analogs) in linear motion. Here's how they relate:


Source: [HSC Physics book & H.C. Verma Vol I – Chapter: Rotational Mechanics]

Gravitational field intensity being zero at a point does not mean there is no gravity or mass. It means that two or more masses are producing gravitational forces in opposite directions, and these forces cancel each other out, resulting in zero net field. However, gravitational potential at that point is not necessarily zero—it may still exist. This concept is often tested in cases like the point between Earth and Moon where gravitational pull balances.

Source: [HSC Physics book & H.C. Verma, Vol. I, Chapter: Gravitation]

In a stable circular orbit, a satellite maintains a constant distance from the planet, so the torque acting on it is zero. Since torque is the rate of change of angular momentum, and torque = 0, angular momentum remains conserved. Kinetic and potential energies may individually vary depending on orbit shape (in elliptical cases), but angular momentum is conserved in both circular and elliptical orbits unless acted upon by an external torque.

Source: [HSC Physics book & H.C. Verma, Vol. I, Chapter: Gravitation]

Rotational kinetic energy depends on both moment of inertia and angular velocity. This formula is fundamental in analyzing spinning systems like engines or gyroscopes.

Source: [HSC Physics book]

Precession is the slow circular motion of the rotation axis. For a top, gravity applies a torque about the point of contact. This causes the axis to rotate, not fall over immediately. The result is a precessional motion—key in gyroscope operation and astronautics.  Why other options are wrong:

• A) Gravity: It's the force, but not the direct cause of precession — torque from gravity is the cause.

• B) Angular velocity: This keeps the top spinning, but doesn’t cause precession.

• D) Friction: Friction slows the top, but not responsible for precession itself.
  
  [Source: Resnick, Halliday & Krane – Physics, Chapter on Rigid Body Rotation]

When the ice skater pulls her arms in while spinning, she is changing her moment of inertia. Angular momentum L=Iω is conserved. When she pulls arms in, moment of inertia (I) decreases, so angular velocity (ω) increases to keep L constant. This phenomenon is a classic example of angular momentum conservation, seen in figure skating and satellite orientation.

Source: [HSC Physics Book]

What Actually Happens:

• A satellite in orbit is constantly falling towards Earth due to gravity.

• But it also has tangential velocity — it moves forward fast enough that as it falls, the Earth curves away beneath it.

• This creates a condition called orbiting, where the satellite is in continuous free fall around the Earth, rather than falling into it.

Why Weightlessness?

• Objects inside the satellite are also in free fall under gravity.

• Since both the satellite and its contents fall at the same rate, no normal force (which we perceive as "weight") is acting between them.

• So, everything floats — this is what we call apparent weightlessness.
  
  Source: [HSC Physics book]

Angular acceleration is negative, indicating deceleration. This concept is used in braking systems, flywheel deceleration, and rotational dynamics modeling.

Source: [HSC Physics book]

This numerical application of Newton’s Law of Gravitation shows the very small magnitude of gravitational force between ordinary masses. Hence, gravitational force is significant only in planetary or large-mass scenarios.

Source: [HSC Physics book]

Gravitational potential is always negative due to the attractive nature of gravity. The zero potential is defined at infinite distance from the mass. As you approach a massive body, potential becomes more negative. A negative potential thus implies the object is within the gravitational influence of a mass and is bound to it unless sufficient energy is provided to escape.

Source: [HSC Physics book]

Due to Earth’s rotation, a centrifugal force acts outward from the axis of rotation. This force is maximum at the equator and zero at the poles. At the equator, the centrifugal force partly counteracts gravity, making the effective gravitational acceleration smaller. At the poles, since there is no centrifugal effect, gravity is stronger.

Also, Earth is not a perfect sphere but an oblate spheroid—flattened at the poles and bulging at the equator. This means the poles are closer to the Earth’s center, which further increases gravitational acceleration there.

Source: [HSC Physics book]

Orbital speed depends on mass of Earth and radius of orbit. It does not depend on satellite’s mass. This formula is fundamental in satellite motion and helps determine satellite positioning and communication orbit parameters.

Source: [HSC Physics book]

Gravity is lowest at the equator due to two reasons:

1. Rotational effect: Maximum centrifugal force at equator reduces effective gravity.

2. Equatorial bulge: The radius is largest at the equator, increasing the distance from the Earth's center.
   These two effects combine to reduce gravity more than any altitude-related effect like that on Mount Everest. Even though Everest is high, the equator still experiences slightly less g.
   
   [Source: [HSC Physics book]

 

A black hole is formed when a massive star collapses under its own gravity, compressing all its mass into an extremely small point called a singularity. Here's what happens in terms of physics:

• Mass: A black hole does not have infinite mass. It has finite mass, which can range from a few solar masses to billions of solar masses.

• Radius: The event horizon (the boundary beyond which nothing can escape) has a measurable, non-zero radius. It's called the Schwarzschild radius, and it increases with mass.

• Gravity: The gravitational pull of a black hole is extremely strong, but not infinite. It is strongest near the singularity.

• Density: The entire mass is concentrated into zero volume (at the singularity). Since density = mass/volume, and the volume approaches zero, the density becomes infinite in theory.

So, infinite density is the correct answer because it’s a result of enormous mass compressed into an almost zero-volume space.


[Source: HSC Physics book & "Concepts of Physics" by H.C. Verma – Volume 2, Chapter: Gravitation]

A gyroscope maintains its orientation due to the conservation of angular momentum. When spinning, it resists changes in its axis of rotation unless acted on by external torque. This is why spinning tops don't fall immediately and why gyroscopes are used in navigation systems.



[Source: HSC Physics 1st Paper (NCTB)]

Uniformly accelerated angular motion means the angular velocity of the flywheel increases at a constant rate due to a constant applied torque. This concept is crucial in flywheel design because:

• It allows predictable and controlled energy storage and release.

• The torque applied to the flywheel can be used more efficiently, optimizing the rotational energy buildup.

• In applications like engines, presses, and energy storage systems, a uniform angular acceleration ensures smoother operation and better performance.
  
  Source: [HSC Physics book]