# I tried India's Hardest Exam

TLDRIn this challenging physics problem, the presenter tackles a question from the GRE Advanced exam involving two stars, A and B, with star B initially twice as massive as A. After an astrophysical event causes B to consume A, star A's radius shrinks to half, and its remaining mass forms a shell around B. The presenter calculates the escape velocities for both stars, deriving a formula to find the ratio of their velocities, ultimately determining the value of n to be 2.3. The detailed explanation showcases the complex process of solving a high-level physics problem, engaging viewers with its depth and clarity.

###### Takeaways

- π The video discusses a challenging physics problem from the GRE Advanced exam, which is known for its difficulty.
- π The problem involves two stars, A and B, with star B initially having twice the mass of star A and different densities.
- π An astrophysical event causes star B to consume star A, leading to star A shrinking and its remaining mass forming a shell around star B with the same density as star A.
- π Star A's new mass is calculated to be one-eighth of its original mass after the consumption process.
- π The new radius of star A is half of its original radius, and the density remains constant.
- π§ The escape velocity formula is re-derived in the video, emphasizing its importance for solving the problem.
- βοΈ The escape velocity of star A (VA) is calculated using the formula and the new mass and radius of star A.
- π For star B, the escape velocity (VB) is calculated considering the new mass after consuming star A and the original radius.
- π’ The mass of star B after the event is the original mass plus seven-eighths of star A's original mass.
- π The new radius of star B is determined by the volume of the spherical shell formed by the remaining mass of star A.
- π The ratio of the escape velocities (VB/VA) is simplified to find the value of 'n', which is the final answer to the problem.
- π― The final calculation reveals that 'n' equals 2.3, solving the GRE Advanced physics problem presented in the video.

###### Q & A

### What is the context of the physics exam mentioned in the script?

-The context is the General Advanced Physics exam, which is considered one of the most challenging physics exams in the world.

### What is the initial condition of Star A and Star B in terms of mass and radius?

-Initially, both Star A and Star B have the same radius, denoted as R. The mass of Star B is initially twice the mass of Star A.

### What happens to Star A due to an astrophysical process?

-Due to an astrophysical process, Star B starts devouring Star A, causing Star A to shrink to half of its original radius.

### How does the density of Star A change after the process?

-The density of Star A remains the same after the process, even though its volume has decreased.

### What is the new mass of Star A after the process, and how is it related to its original mass?

-The new mass of Star A, denoted as m_a dash, is one-eighth of its original mass, m_a.

### What formula is used to calculate the escape velocity of a star?

-The escape velocity formula used in the script is derived from setting the kinetic energy equal to the gravitational potential energy at the star's surface.

### How is the escape velocity of Star A, VA, calculated in the script?

-VA is calculated by setting the kinetic energy (1/2 m v^2) equal to the gravitational potential energy (GMm/R), where M is the mass, m is the reduced mass of Star A, and R is the new radius.

### What is the new mass of Star B after devouring Star A?

-The new mass of Star B is the original mass of Star B plus 7/8 of the original mass of Star A.

### How does the volume of the shell around Star B relate to the original volume of Star A?

-The volume of the shell is the difference between the volume of the new Star B and the original volume of Star A.

### What is the final expression for the ratio of the escape velocities of Star B to Star A (VB/VA)?

-The final expression for the ratio VB/VA is derived to be 23/(cube root of 15), indicating that n equals 2.3.

### What conclusion is reached regarding the value of n in the given expression for the ratio of escape velocities?

-The conclusion is that n equals 2.3, based on the derived expression for the ratio of the escape velocities of the two stars.

###### Outlines

##### π Astrophysical Star Devouring Problem

This paragraph introduces a complex physics problem involving two stars, A and B, where star B has twice the mass of star A. Star A shrinks to half its radius after being consumed by star B, while maintaining its density. The problem requires calculating the escape velocity ratio (Vb/Va) of the stars using the given densities and masses. The solution involves deriving the new mass of star A and using the escape velocity formula, which is re-derived for clarity. The process includes setting up kinetic and gravitational energy equations and simplifying them to find the escape velocities for both stars.

##### π Calculating Escape Velocities and Star Radii

The second paragraph delves into the calculations of the escape velocities for both stars after the astronomical event. It starts by determining the new mass of star A and its escape velocity using the rearranged kinetic and gravitational energy equations. The process then moves on to calculate the escape velocity for star B, considering the increase in its mass due to consuming star A. The key to solving this part of the problem is understanding the volume and density of the spherical shell formed around star B, which leads to finding the new radius of star B. The calculations are meticulous, involving algebraic manipulations to isolate and solve for the variables.

##### π― Solving for the Escape Velocity Ratio and Final Answer

The final paragraph wraps up the problem by calculating the ratio of the escape velocities (Vb/Va). It begins with simplifying the expressions for the escape velocities of both stars and then finding the ratio. The solution process involves careful algebraic manipulation to cancel out terms and isolate the variable n, which represents the power in the given expression for the escape velocity ratio. After significant work, the paragraph concludes with the discovery that n equals 2.3, solving the problem and providing a sense of satisfaction in tackling a challenging physics question.

###### Mindmap

###### Keywords

##### π‘Physics exam

##### π‘Stars

##### π‘Density

##### π‘Astrophysical process

##### π‘Escape velocity

##### π‘Spherical shell

##### π‘Volume

##### π‘Mass

##### π‘Gravitational constant

##### π‘Ratio

##### π‘Cube root

###### Highlights

Introduction to the challenging G Advanced Physics exam, emphasizing the time constraint of two minutes per question.

Description of the problem involving two stars with initial equal radii and different densities, with Star B having twice the mass of Star A.

Explanation of an astrophysical process where Star B starts devouring Star A, causing Star A to shrink and its mass to redistribute.

Derivation of the new mass of Star A after the process, which is one-eighth of its original mass.

Calculation of the escape velocity for Star A using the formula for kinetic energy set equal to gravitational potential energy.

Introduction of the formula for escape velocity and the recommendation to memorize it for quick recall during exams.

Rederivation of the escape velocity formula for Star A, taking into account the new mass and radius.

Calculation of the escape velocity for Star B, considering the new mass after devouring Star A and the original radius.

Explanation of the mass change in Star B after the devouring process, including the acquisition of mass from Star A.

Derivation of the new radius of Star B using the density of the spherical shell formed after the process.

Calculation of the volume of the shell and its relation to the new radius of Star B.

Final calculation of the escape velocity for Star B using the new radius and adjusted mass.

Determination of the ratio of the escape velocities of Star B to Star A (VB/VA) and the expression for n.

Simplification of the ratio expression, leading to the conclusion that n equals 2.3.

Reflection on the problem-solving process and the satisfaction derived from solving complex physics problems.

Encouragement for viewers to explore more problems from the G Advanced exam for further practice.

###### Transcripts

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