A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and the string vibrates forming 8 loops. When the stone is immersed in water 10 loops are formed. The specific gravity of the stone is close to  
A)  1.8
B)  4.2
C)  2.8
D)  3.2

correct option is C)  2.8

Step-by-step explanation:

given data

string vibrates form =  8 loops

in water loop formed =  10 loops

solution

we consider  mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone =

case (1)  

when 8 loop form with 2 adjacent node is

so here

     ..............1

and we know velocity is express as

velocity = frequency × wavelength   .....................2

  =   f ×

here tension = mg

so

  =   f ×     ..........................3

and

case (2)  

when 8 loop form with 2 adjacent node is

     ..............4

when block is immersed

equilibrium  eq will be

Tenion + force of buoyancy = mg

T + v × × g = mg

and

T = v × - v × × g    

from equation 2

f × = f  ×  

    .......................5

now we divide eq 5 by the eq 3

solve irt we get

so

relative density

relative density = 2.78 ≈ 2.8

so correct option is C)  2.8

the answer will be