х

66. Two masses m1 and m, balance each other when weighed in water; the specific gravity of the one being S1, what is that of the other?

67. A piece of silver (specific gravity= 10.5) weighing 20 grammes and a piece of tin (specific gravity= 7.3) are fastened to the two ends of a string passing over a pulley, and hang in equilibrium when entirely immersed in water: determine the weight of the tin.

68. What should be the weight of the piece of tin in the preceding example, in order that both bodies might hang in equilibrium when immersed in a liquid of specific gravity 1.5?

69. A string is passed over a pulley so that one end hangs in a beaker of water and the other in a beaker containing salt solution of specific gravity 1.281. A

lump of copper (specific gravity 8.9) is hung from one XX

end of the string so as to be immersed in the water:
what weight of lead of specific gravity 11.4 must be
attached to the other end of the string so as to keep the
copper in equilibrium when the lead is completely im-
mersed in the salt solution?

70. Find the acceleration with which a stone of
specific gravity 2.8 would sink in water, and the time
which it would take to get to the bottom of a pool 16
feet deep.

71. A 7-lb. iron weight (specific gravity 7.3) is suspended from one end of an equal-armed lever and immersed in water: what weight must be hung from the other end of the lever in order to counterpoise it?

72. A cube of gutta-percha (specific gravity 0.96), two centimetres in the side, is suspended from the short

pan of a hydrostatic balance, and a basin of water placed beneath: what weight must be placed upon th pan in order that there may be equilibrium when th gutta-percha is completely immersed ?

73. State the conditions which must be fulfilled order that a body may float in equilibrium in a liqui and show that if a homogeneous body of volume v an specific gravity s floats in a liquid of specific gravity the volume of the part immersed will be

74. What volume of water will be displaced by kilogramme of wood of specific gravity 0.75 floating equilibrium?

75. A piece of cork of mass 300 grammes and densi 0.25 is placed in a vessel full of water: how much wat will overflow?

76. The specific gravity of ice is 0.918 and that sea-water is 1.03: what is the total volume of an ic berg which floats with 700 cubic yards exposed?

77. A sphere of density 0.95 and volume 100 cub Oil of density 0.9 is poure centimetres floats on water. upon the water, the layer of oil being deep enough cover the sphere: how much of it will now be immers in the water?

78. A solid body floats in water with just half i volume immersed. When it floats in a mixture of equ volumes of water and another liquid, one-third of it immersed: find the specific gravities of the solid a liquid.

79. A sphere of glass (density 2.8) is dropped into vessel containing mercury and water: find its positio of equilibrium.

80. A solid weighs 100 grammes in air and grammes in a liquid of specific gravity 1.2: what is i specific gravity?

81. A body weighs 124 grammes in vacuo, 10

grammes in water, and 98 grammes in another liquid: what is the specific gravity of the liquid?

82. A solid which weighs 120 grammes in air is found to weigh 90 grammes in water and 78 grammes in a strong solution of zinc sulphate: what is the specific gravity of the solution?

83. A specific gravity bottle weighs 14.72 grammes when empty, 39.74 grammes when filled with water, and 44.85 grammes when filled with a solution of common salt: what is the specific gravity of the solution?

84. A specific gravity bottle when filled with water weighs 61.485 grammes, and when filled with methylated spirit 53.462 grammes. If the bottle weighs 15.063 grammes what is the specific gravity of the spirit?

85. In a determination of the specific gravity of a saturated solution of zinc sulphate with the same bottle, the weight of the bottle filled with water was 61.460 grammes, and, when filled with a solution at 14.6°C., 81.559 grammes: find the specific gravity of the solution at this temperature.

86. Find the specific gravity of a mixture of methylated spirit and water from the following data :

87. A specific gravity bottle was found to weigh 39.74 grammes when filled with water. Some iron nails weighing 8.5 grammes were introduced, and the bottle was again filled up with water. The weight now was 47.12 grammes: show that the specific gravity of the iron nails was 7.59.

88. After removing the nails from the bottle, 40.37 grammes of lead shot was introduced, and after filling up with water, the weight of the whole was 76.54

grammes • what was the specific gravity of the chat

89. Find the specific gravity of monoclinic sulp from the following data:

0.5260 gn

90. A solid, lighter than water, and weighing grammes in air, is fastened to a piece of metal, and combination is found to weigh 36 grammes in water the piece of metal weighs 45 grammes in water, wha the specific gravity of the light solid?

91. Find the specific gravity of a given solid fr the following data:

0.5 gn

4.0 99

92. A sinker weighing 38 grammes is fastened t piece of cork weighing 10 grammes, and the two toget just sink when placed in water: find the spec gravity of the sinker, taking that of cork as 0.25.

93. In order to determine the specific gravity o piece of fluor-spar, it was placed upon the upper par a Nicholson's hydrometer, and weights were added u the instrument sank to a fixed mark in the stem. removing the fluor-spar an additional weight of 9 This additional weight grammes had to be added.

next taken off and the spar placed in the lower
(immersed in water), when it was found that 3
grammes had to be placed in the upper pan to sink
hydrometer to the same mark: what was the spec
gravity of the spar?

94. A Nicholson's hydrometer, when floating water, required a weight of 0.15 gramme to be pla upon the upper dish in order to make it sink to a fi mark on the stem; and 5.72 grammes had to be pla

hur

n.

25

the

: if at is

From

n.

to a :her cific

upon the dish in order to make it sink to the same mark in a solution of salt. If the hydrometer weighed 94.47 grammes, what was the specific gravity of the solution?

95. Walker's specific gravity balance consists of a lever with unequal arms; a fixed weight is hung from the shorter arm, and the longer arm is graduated in inches and tenths of an inch. The lever rests on a knife-edge at X, and is horizontal when a body is suspended in air from a point Y on the long arm; when it is immersed in water the point of suspension has to be moved to Z in order to obtain equilibrium: show that the specific gravity of the body is

XZ/(XZ - XY).

96. The specific gravity of a piece of solder was determined by Walker's balance. When weighed in air the length of the arm (or distance of the point of suspension from the knife-edge) was 11.05 inches; when weighed in water the length of the arm was 12.55 inches: show that the specific gravity of the solder was 8.37.

97. In order to find the specific gravity of a mineral two experiments were made, the position of the weight on the short arm being altered after the first determination.

Substance weighed in air

of a 1 of

ntil

On .85

was

Exp. I. {
Exp. II.

pan

.06

the

ific

in

ced

xed

Length of Arm.

5.78 in.

Show that the mean result of the two experiments is 2.751.

98. The lever of a Walker's balance is in equilibrium when a body is suspended from a point Y on the long arm, the fulcrum being at X. When the body is immersed in water the point of suspension is at Z, and when it is immersed in another liquid the naint