A stone is suspended from a spring balance with a fine thread. The readings of the spring balance when the stone is in air and in liquid are $0.065 k g a n d 0.052 k g$ , respectively. Calculate the density of liquid if the density of material of stone is $5200 k g / m^{3}, g = 9.8 m / s^{2}$ .

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Solution

Step 1: Given data,
Mass of the stone in air = $0.065 k g$
So, the weight of the stone in air = $0.065 k g \times 9.8 m / s^{2} = 0.637 N$
Mass of the stone in liquid = $0.052 k g$
So, the weight of the stone in liquid = $0.052 k g \times 9.8 m / s^{2} = 0.51 N$
The density of the stone = $5200 k g / m^{3}$
Acceleration due to gravity = $g = 9.8 m / s^{2}$
Step 2: Finding the density of the liquid,
$R e l a t i v e d e n s i t y = \frac{w e i g h t o f s t o n e i n a i r}{w e i g h t o f s t o n e i n a i r - w e i g h t o f s t o n e i n l i q u i d} = \frac{0.637 N}{0.637 N - 0.51 N} = 4.98 A l s o, r e l a t i v e d e n s i t y = \frac{d e s n i t y o f s t o n e}{d e n s i t y o f l i q u i d} S o, d e n s i t y o f l i q u i d = \frac{d e s n i t y o f s t o n e}{r e l a t i v e d e n s i t y} = \frac{5200 k g / m^{3}}{4.98} = 1040 k g / m^{3}$
Hence, the density of the liquid is $1041 k g / m^{3}$ .

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A stone is suspended from a spring balance with a fine thread. The readings of the spring balance when the stone is in air and in liquid are 0.065kgand0.052kg, respectively. Calculate the density of liquid if the density of material of stone is 5200kg/m3,g=9.8m/s2.

A stone is suspended from a spring balance with a fine thread. The readings of the spring balance when the stone is in air and in liquid are $0.065 k g a n d 0.052 k g$ , respectively. Calculate the density of liquid if the density of material of stone is $5200 k g / m^{3}, g = 9.8 m / s^{2}$ .