MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

  • Complete Physics Course - Class 11
  • OFFERED PRICE: R 2,800
  • View Details
Get extra R 560 off
USE CODE: MOB20

				   

Somebody made a giant spherical cavity in the earth such that the earth's center and a point in the surface are diametrically opposite.

The someone drops a small ball from a small opening at the surface into the cavity. In how many minutes does the ball reach the center of earth???         

6 years ago

Share

Answers : (2)

										

Dear Amrit Pal,


Ans:- Hi first of all I must say that you see the answer of the question. because it is a conceptual and if the solution is not correct then I will also have to attempt it in another way.


Let us consider some terms


Mass of the earth=M


Density of the earth=d


Universal gravitational constant=G


radious of the earth=R


mass of the particle is=m


Now you must know that the value of the gravitational acc g′ at a depth h inside the earth is=(1- h/R)g


where g is it's value on the surface of the earth. g=GM/R² and hence  the total force is= 4/3 ∏GmRd(1 - h/R)


F=4/3 ∏Gmd(R-h)..............(1)


Now the value we are getting is due to the superposition of the cut out mass and the remaining mass.


HenceF=Fr+Fc..............(2)


Fr=force due to the remaining and Fc=force due to the cut out


Using eq 1 we can find out the force due to the cut out portion which is Fc=4/3∏ Gmd (R/2 - h)....................(3)


Putting these values of eq 1 and 3 in 2 we get,


Fr=F-Fc


=4/3 ∏Gmd{(R-h)-(R/2 -h)}


=2/3 ∏GmRd


Which is constant i.e h independent


then the acceleration due to this portion is a=Fr/m=2/3 ∏ GRd


So the time taken is t=√{(2R/2)/(2/3 ∏ GRd)}


=√{3/(2GR∏d)}


 


 


Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We
are all IITians and here to help you in your IIT JEE preparation.



All the best Amrit Pal !!!


 



Regards,


Askiitians Experts
Soumyajit Das IIT Kharagpur

6 years ago
										

Dear Saumyajit,


we know that radius of earth is 6400km or 6400000m.


So, in the mouth of the cavity, the ball is at a potential=mgh.


and, at the centre, it will have the KE=mv2/2.


Equating both.


mgh=mv2/2, where h=6400000m.


by this, we get, v=11200m/s.


now, u may apply the first eq. of motion to find the time taken.

6 years ago

Post Your Answer

Other Related Questions on Wave Motion

what is wave intensity............................................?
 
 
DEAR MOHAN, WAVE INTENSITY IS KNOWN AS THE INTENSITY OF THE INTERFERENCE OF THE WAVES IS CALLED A WAVE INTENSITY........................
 
Gowri sankar one year ago
 
In the SI system, it has units watts per square metre (W/m 2 ). It is used most frequently with waves (e.g. sound or light), in which case the average power transfer over one period of the...
 
ULFAT 10 months ago
 
Wave intensity is the average power that travels through a given area as the wave travels through space. The intensity of sound waves is measured using the decibel scale. Let`s talk about...
 
sreekanth sree one year ago
what is antinode ?
 
 
the position of maximum displacement in a standing wave system.
 
KUNCHAM SAMPATH one year ago
 
the position of maximum displacement in a standing wave system.
 
pa1 one year ago
 
the position of maximum displacement in a standing wave system.
 
RAKESH CHINDAM one year ago
What are harmonics?
 
 
Dear Prabhakar, Harmonic is the wave or signsl whose frequency is an integral multiple of prequency of some reference signal or wave.
 
SAI SARDAR one year ago
 
Hello Prabhakar, We noticed that you are misuing the rights of questioner given by forum and approving all the answers of all the users even if it is written garbage which has no connection...
 
Forum Team one year ago
 
hello prabhakar... A harmonic is a signal or wave whose frequency is an integral (whole-number) multiple of the frequency of some reference signal or wave. The term can also refer to the...
 
mohan one year ago
what is work energy thereom...................................?
 
 
The work-energy theorem is a generalized description of motion which states that work done by the sum of all forces acting on an object is equal to change in that object’s kinetic energy....
 
dolly bhatia one month ago
 
The work W done by the net force on a particle equals the change in the particle`s kinetic energy KE: W = Δ K E = 1 2 m v f 2 − 1 2 m v i 2 . The work-energy theorem can be derived from...
 
Sushmit Trivedi one month ago
 
For any net force acting on a particle moving along any curvilinear path, it can be demonstrated that its work equals the change in the kinetic energy of the particle by a simple derivation...
 
rahul kushwaha 3 months ago
The cieling of long hall is 25 m high What is the maximum horizontal distance that a ball thrown with a speed of 40 ms can go without hitting the ceiling of wall? Plz explain with a DIAGRAM
 
 
Let the angle of throwing be Q with respect to the ground So, the range is R = 40*cosQ*t where t = time taken reach ground. Now, we know the time taken to reach the top of its flight is half...
 
Tapas Khanda 5 months ago
 
Let the angle of throwing be Q with respect to the ground So, the range is R = 30*cosQ*t where t = time taken reach ground. Now, we know the time taken to reach the top of its flight is half...
 
Tapas Khanda 5 months ago
 
Diagram is not required to solve this question. You can directly use the formula to find range : R = (v^2/g)*sin2Q Maximum height reached, H = v^2*sin^2Q/2g So, 25 = 40^2*sin^2Q/(2*9.8) So,...
 
Tapas Khanda 5 months ago
What harmfull gases are produced when we burn plastics? And can we burn plastics?
 
 
I`m doing a project, can someone help me, How to reduce those toxic contents when plantic are burnt Like sulphur, nitrogen etc
 
2017 years ago
 
nitrogen gas , sulphur dioxide ,carbon monoxide , carbon dioxide. are some of the gases. well burning plastic is not good for living things. but there are many other things that are more...
 
2 days ago
View all Questions »

  • Complete Physics Course - Class 12
  • OFFERED PRICE: R 2,600
  • View Details
Get extra R 520 off
USE CODE: MOB20

  • Complete Physics Course - Class 11
  • OFFERED PRICE: R 2,800
  • View Details

Get extra R 560 off
USE CODE: MOB20

More Questions On Wave Motion

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details