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Question

A certain block weighs 22 N in air. It weighs 17 N when immersed in water. When immersed in another liquid it weighs 18 N. Calculate the relative density of the other liquid.

A
0.8
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B
0.67
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C
0.2
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D
1
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Solution

The correct option is A 0.8
Let the relative density of the block be rb and that of the liquid be rl
Density of water be ρ
Density of metal is rbρ and density of liquid is rlρ

Let the volume of the block be V

Weight of the block in air is W1=rbρVg=22N
Weight of the block in water is W2=(rb1)ρVg=17N
Weight of the block in the liquid is W3=(rbrl)ρVg=18N

Thus, dividing W2 by W1, we get
W2W1=rb1rb=1722rb=225=4.4

Dividing W3 by W1, we get
W3W1=rbrlrb=18224.4rl4.4=911rl=0.8

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