In Melde's experiment , when a string is stretched by a piece of glass it vibrates with7 loops . When the glass piece is completely immersed in water the string vibrates in9 loops. What is the specific gravity of glass ?

In Melde's experiment , when a string is stretched by a piece of glass

1.	In Melde's experiment , when a string is stretched by a piece of glass it vibrates with7 loops . When the glass piece is completely immersed in water the string vibrates in9 loops. What is the specific gravity of glass ?
Answer» <P> SOLUTION :If `F_(1) and F_(2)` are the TENSIONS in the strings in the two cases , then `F_(1) p_(1)^(2) = F_(2) P_(2)^(2)` `(F_(1))/(F_(2)) = (P_(2)^(2))/(P_(1)^(2)) = ( 9^(2))/( 7^(2)) = ( 81)/( 49)` If `F_(b)` is the buoyant force on the GLASS piece , then ` F_(b) = F_(1) - F_(2)` Specific gravity of glass ` = ( "Weight in AIR" )/( "Loss in weight in water" )` ` = (F_(1))/( F_(b)) = (F_(1))/( F_(1) - F_(2)) = (1)/( 1 - (F_(2))/(F_(1)))` `(1)/( 1- ( 49)/( 81)) = 2.53`