An object with uniform density $ρ$ attached to a spring that is known to stretch linearly with applied force as shown above.
When the spring object system is immersed in a liquid of density $ρ$ , as shown in the figure, the spring stretches by an amount $x_{1} (ρ > ρ_{1})$ . When the experiment is repeated in a liquid of density $ρ_{2} < ρ_{1}$ , the spring stretches by an amount $x_{2}$ . Neglecting any buoyant force on the spring, the density of the object is :

Question

Q. An object with uniform density

ρ

is attached to a spring that is known to stretch linearly with applied force as shown below.
When the spring-object system is immersed in a liquid of density

ρ_{1}

as shown in the figure, the spring stretches by an amount

x_{1} (ρ > ρ_{1})

. When the experiment is repeated in a liquid of density

ρ_{2} < ρ_{1}

. the spring stretches by an amount

x_{2}

. Neglecting any buoyant force on the spring, the density of the object is

Answer 1

k x_{1} + ρ_{1} v g = ρ v g

Answer 2

v = \frac{k x_{1}}{ρ g - ρ_{1} v g}

Answer 3

k x_{2} + ρ_{2} v g = ρ v g

Answer 4

v = \frac{k x_{2}}{ρ g - ρ_{2} v g}

Answer 5

\frac{k x_{1}}{(ρ - ρ_{1}) g} = \frac{k x_{2}}{(ρ - ρ_{2}) g}

Answer 6

ρ x_{1} - ρ_{2} x_{1} = ρ x_{2} - ρ_{1} x_{2}

Answer 7

ρ (x_{1} - x_{2}) = ρ_{2} x_{1} - ρ_{1} x_{2}

Answer 8

ρ = \frac{ρ_{2} x_{1} - ρ_{1} x_{2}}{x_{1} - x_{2}}

Answer 9

Hence, the correct option is

B

The correct option is B ρ=ρ1x2−ρ2x1x2−x1kx1+ρ1vg=ρvgv=kx1ρg−ρ1vgkx2+ρ2vg=ρvgv=kx2ρg−ρ2vgkx1(ρ−ρ1)g=kx2(ρ−ρ2)gρx1−ρ2x1=ρx2−ρ1x2ρ(x1−x2)=ρ2x1−ρ1x2ρ=ρ2x1−ρ1x2x1−x2Hence, the correct option is B