Physics, 12.09.2019 19:30, kitttimothy55

In an experiment, a rectangular block with height h is allowed to float in two separate liquids. in the first liquid, which is water, it floats fully submerged. in the second liquid it floats with height h/7 above the liquid surface. what is the relative density (the density relative to that of water) of the second liquid?

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answered: Gattuso

The relative density of the second liquid is 7.

Explanation:

From archimede's principle we know that the force that a liquid exerts on a object equals to the weight of the liquid that the object displaces.

Let us assume that the volume of the object is 'V'

Thus for the liquid in which the block is completely submerged

The buoyant force should be equal to weight of liquid

Mathematically

$F_{buoyant}=Weight\\\\\rho _{1}\times V\times g=m\times g\\\\\therefore \rho _{1}=\frac{m}{V}...............(i)$

Thus for the liquid in which the block is 1/7 submerged

The buoyant force should be equal to weight of liquid

Mathematically

$F'_{buoyant}=Weight\\\\\rho _{2}\times \frac{V}{7}\times g=m\times g\\\\\therefore \rho _{2}=\frac{7m}{V}.................(ii)$

Comparing equation 'i' and 'ii' we see that

$\rho_{2}=7\times \rho _{1}$

Since the first liquid is water thus $\rho _{1}=1gm/cm^3$

Thus the relative density of the second liquid is 7.

answered: Guest

the amount of current in the coil

answered: Guest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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In an experiment, a rectangular block with height h is allowed to float in two separate liquids. in...