Mechanical Properties Of Solids

To solve this problem, let's consider the forces and torques acting on the ladder. The ladder is supported on a rough floor and leans against a smooth wall. The key forces acting on the ladder are:

• The gravitational force acting at the center of the ladder.
• The normal force from the wall, which acts horizontally.
• The normal force from the floor, which acts vertically.
• The frictional force at the base of the ladder, acting horizontally.

The ladder is at the verge of slipping when the static frictional force . Let be the length of the ladder. The torque balance about the point where the ladder touches the floor gives us:
For the ladder to be in equilibrium, the sum of vertical forces and horizontal forces must be zero. Thus:
Since :
Thus, . Substituting this into the torque balance equation results in:
Simplifying, this equation becomes:
Rearranging and solving for yields:
Simplifying further, and recognizing that the remaining torque relation allows us to solve for :
Therefore, the horizontal distance moved by the man:

The primary source of energy in the Sun is the conversion of hydrogen into helium in a nuclear fusion reaction. This process occurs in the Sun's core and is known as the proton-proton chain reaction. Here is a step-by-step explanation of how this energy is generated:

1. Nuclear Fusion: At extremely high temperatures and pressures in the Sun's core, hydrogen nuclei (protons) overcome their mutual electrostatic repulsion and fuse together. This is due to the intense gravitational pressure compressing the core.
2. Fusion Process: The fusion process primarily involves several steps where hydrogen nuclei are converted into helium. The primary reactions in the proton-proton chain are:
   
3. Step 1: Two protons collide, and one converts into a neutron via beta-plus decay, forming a deuteron (a nucleus of deuterium, i.e., heavy hydrogen). This reaction releases a positron and a neutrino.
4. Step 2: The deuteron then fuses with another proton, forming helium-3 and releasing gamma radiation.
5. Step 3: Two helium-3 nuclei collide to form helium-4, releasing two protons.
   The net effect of these reactions is that four hydrogen nuclei (protons) combine to form one helium nucleus, and this process releases a significant amount of energy.
6. Energy Release: The energy released during each fusion reaction propagates outward from the core. This energy travels through the radiative and convective layers of the Sun and eventually reaches the photosphere, where it is emitted as sunlight.

This mechanism of hydrogen fusion into helium is the process that powers the Sun and other stars, making it the correct answer.