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A stone is hung in air from a wire which is stretched over a sonometer . The bridges of the sonometer are 40 cm apart when the wire is in unison with a tuning fork of frequency 256. When the stone is completely immersed in water, the length between the bridges is 22 cm for re-establishing unison. The specific gravity of the material of the stone is : |
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Answer» `256 XX (40)/(22)` Tension, `"" T = `Weight of stone. `therefore` In AIR `v_(1) = (1)/(2l_(1)) sqrt((W_(a))/(m))` In water `v_(2) = (1)/(2l_(2)) sqrt((W_(W))/(m))` SINCE ` v_(1) = v_(2) ` `therefore (1)/(2l_(1)) sqrt((W_(a))/(m)) = (1)/(2l_(2)) sqrt((W_(w))/(m))` `rArr "" (W_(a))/(W_(w)) = (I_(1)^(2))/(I_(2)^(2))`. Now relative density of stone = ` (w_(a))/(W_(a) - W_(w))` `therefore` Relative density = `(1)/(1 - (W_(w))/(W_(a)) ) = (1)/( 1 - (I_(2)^(2))/(I_(1)^(2)))` = `(I_(1)^(2))/(I_(1)^(2)- I_(2)^(2)) = ((40)^(2))/((40)^(2)- (22)^(2) ) `. Correct choice is c. |
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