JEE Exam > JEE Questions > Consider a uniform spherical planet of mass M...
Start Learning for Free
Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest?
Most Upvoted Answer
Consider a uniform spherical planet of mass M and radius R. two parall...
Solution:
Understanding the problem
To understand the problem, let us consider the following points:
- A uniform spherical planet of mass M and radius R is at rest.
- Two parallel tunnels are dug at a perpendicular distance of 3R/5 symmetrically from the centre of the planet.
- A particle is thrown from one tunnel such that it enters the other tunnel without making a collision with the tunnel wall.
- The tunnels are frictionless, and the particle just lifts inside the tunnel.
Analyzing the problem
To analyze the problem, we need to consider the following:
- The force acting on the particle is the gravitational force due to the planet.
- As the planet is uniform, the gravitational force will be the same throughout the planet.
- The tunnel is frictionless, so no external force will act on the particle once it enters the tunnel.
- The particle will move in a straight line unless acted upon by an external force.
Calculating the trajectory
To calculate the trajectory of the particle, we need to consider the following:
- The particle will follow a parabolic path from the starting point to the other tunnel.
- The particle will experience an acceleration due to gravity towards the centre of the planet.
- As the tunnels are dug symmetrically, the particle will take the same time to reach the other tunnel.
- The velocity and the angle at which the particle is thrown will determine the trajectory of the particle.
Finding the conditions for the particle to enter the other tunnel
To find the conditions for the particle to enter the other tunnel, we need to consider the following:
- The particle should enter the other tunnel without making a collision with the tunnel wall.
- The distance between the two tunnels is known, and the radius of the planet is known.
- The angle at which the particle is thrown and the velocity should be such that the particle enters the other tunnel without making a collision.
Conclusion
In conclusion, the trajectory of the particle can be calculated by considering the gravitational force, acceleration, and time taken to reach the other tunnel. The conditions for the particle to enter the other tunnel can be determined by considering the distance between the tunnels, the radius of the planet, and the angle and velocity at which the particle is thrown.
Community Answer
Consider a uniform spherical planet of mass M and radius R. two parall...
Consider a uniform spherical planet of mass M and radius R. Two parallel tunnels are dug at 3R perpendicular distance symmetrically from centre. A particle is to be thrown from the starting of one tunnel such that it enters in another tunnel without making collision with tunnel wall and continues its motion as shown in figure. Tunnels are friction less and particle just fits inside the tunnel. Consider the planet to be at rest. 3R 3R Choose the correct options. (A) Speed with which the particle is to be thrown at starting of one tunnel is GM (B) Minimum speed of particle during entire motion is VOR (C) Maximum height achieved by the particle during subsequent motion is (D) Speed with which the particle is to be thrown at starting of one tunnel is
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest?
Question Description
Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest?.
Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest?.
Solutions for Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest? defined & explained in the simplest way possible. Besides giving the explanation of
Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest?, a detailed solution for Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest? has been provided alongside types of Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest? theory, EduRev gives you an
ample number of questions to practice Consider a uniform spherical planet of mass M and radius R. two parallel tunnels are dug at perpendicular distance 3R/5 symmetrically from centre . A particle is to be thrown from the starting one tunnel such that it enters into another tunnel without making collision with tunnel wall and continuous its motion as shown in the figure tunnels are frictionless and particle just lifts inside the tunnel. Consider the planet to be at rest? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup