IIT JEE , AIEEE Forum - Physics , Mechanics

(2)

length of spring is a when 4N force is applied on it. Its length is b when 5N force is applied. Then length of spring when 9N force is applied is _________

explanation detailed required

rohitju

is the answer a+b?

INDIAN_ARMY19890

very simple
u know F=kx
put F=4N and x=a
u will get 4=ak..........1
put F=5N and x=b u will get
5=bk...........2
now we have F=9N and let lenght be Z
9=kZ.............3 u can easliy get value of Z
Z=9a/4 or 9b/5

INDIAN_ARMY19890

the answer will be
Z=45a+36b/40

TigerEyes

The Answer is : 5b - 4a

The mistake that Indian Army has made is that he assumed x to be the final length of the spring which is incorrect because x is the extension produced and not the final length.

so the solution goes this way:

Let the initial length of the spring be : L, then

by F=Kx

Case1

F=4 , x = a-L

4=K(a-L) ............ (1)

Case2

F=5, x=b-L

5=K(b-L) ................ (2)

dividing (1) by (2) and cross multiplication,

we get L = 5a-4b

now,

case3

F=9, let final length be z

then x = z-L

=> 9=K(z-L) ................. (3)

subsitute for K,

and divide (3) by (2) after substiting for L

and solve for z

z comes out to be : 5b-4a.

INDIAN_ARMY19890

i think a and b are elongation

TigerEyes

oops , mistake, after equation (3) plz substitute for L .. i wrote K by mistake

thnx

shubham.123

i agree with tiger eyes reply..................

INDIAN_ARMY19890

if a and b are elongations then u r wrong tiger
12345 make it clear what is a and b here

INDIAN_ARMY19890

if a abd b are not elongation but natural lenght then k will be =1/b-a

INDIAN_ARMY19890

L(natural lenght)=5a-4b hence
X(elongation when 9N force is applied =9(b-a)
total lenght when 9N force applied=X+L

TigerEyes

Dear Indian Army,

ure right that K=1/b-a, but if this is true then L = 5a-4b. Not 4b-3a.

the answer still remains the same ie . 5b-4a

INDIAN_ARMY19890

ok bro let me check

INDIAN_ARMY19890

yes u r right there was a calculation mistake

TigerEyes

Thank You!

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