MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 11
        
Show that the gravitational field inside the cavity is uniform(same magnitude and direction) and find its value
11 months ago

Answers : (1)

Arun
15841 Points
							

The gravitational field produced by a sphere of uniform density rho at a radius r inside the sphere is radially downward and has magnitude F = Kr where K = G(4/3)pi rho = (GM/R^3). This follows from the fact that the field is the same as if all the mass from 0 to r (e.g. rho * (4/3) pi r^3) were concentrated at the center. Of course the mass above r doesn't contribute. This can also be written as a vector equation F = -Kr where r is the radius vector from the center to the point. 

Now consider any point P within the cavity. Let r be the vector displacement from the center of the big sphere to P. Let S be the vector displacement from the center of the big sphere to the center of the cavity (|S| = R/2). 

The field at P is the same as the field produced by a solid sphere of radius R minus the field produced by the smaller (removed) sphere of radius R/2. The displacements of P from the centers of the two spheres are respectively: r and r-S, so the total field is: 

F = -Kr-(-K(r-S)) = -KS 

In other words the gravitational field everywhere in the cavity is parallel to the axis connecting the center of the cavity to the center of the big sphere, and has the same magnitude (KR/2) as the surface gravity of a solid sphere of radius R/2. Another way of putting it is that the gravity is the same as it would be at the center of the cavity if there were no cavity.
11 months ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Get Extra Rs. 1,590 off

COUPON CODE: SELF10


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 18 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Get Extra Rs. 64 off

COUPON CODE: SELF10

Ask Experts

Have any Question? Ask Experts

Post Question

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