Q#1 only plz show all the work. Consider a beaker filled partially with water si

Question

Q#1 only plz show all the work.

Consider a beaker filled partially with water sitting on a scale. The scale reads w_b, the total weight of the beaker and its water in air (Figure 1a). An object of mass m and volume V attached to a massless string is then lowered into the water until it is fully submerged (Figure 1b). The scale now reads w_b*>w_b. Show that the buoyant force B acting on the object is given by B = w_b* - w_b. Show that the volume V of the object is given by V where rho_water is the density of the water and g is the acceleration of gravity. Show that the density p of the object is given by

Explanation / Answer

here,

wb is reading in figure a and wb is reading in figure b

as the object is immersed in water

a buoyant force acts on the object

so, by the third law of Newton

the object also exerts a force in the liquid that equals to buyont force

1.

so we can say that

buoyant force , B = wb* - wb

2.

buoyant force , B = V * p * g

V is the volume of object

p is the density of water

then

V * p * g = wb* - wb

V = ( wb* - wb)/( p * g)

3.

as we know

Volume of the object = mass of object / density of the object

V = m/p0

putting in the equation

m / p0 = ( wb* - wb)/( p * g)

p0 = m * g * p /( wb* - wb)

the density of the object p0 = m * g * p /( wb* - wb)

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