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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?
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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.
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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
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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?
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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?.
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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
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