A spherical object with a mass = 500 grams and diameter d=20 cm is held fully un

Question

A spherical object with a mass = 500 grams and diameter d=20 cm is held fully under water. calculate the weight ( W) of the object. Calculate the buoyancy force (FB). Show all your work (Hence: To calculate the buoyancy, we need the volume of displaced water, which is the volume of the ball because it is being held completely submerged: V obj=(4/3.) pi R^3. Now, apply Archimedes' principle. Density of the water is: rho= 1000kg/m^3) When released, does the object sink to the bottom or float to the surface? (Hence , you need to compare density of water and the density of the object)

Explanation / Answer

mass of the object m=500 g =0.5 kg

diameter of the object d=20cm

radius of the object r=10cm=0.1 m

volume of the object V=4/3*pi*r^2

V=4/3*pi*0.1^3

V=4.19*10^-3 m^3

a)

weight of the object in air W1=m*g

w1=0.5*9.8

w1=4.9 N

b)

if the object is in water,

upthrust is buoyant force FB=rho_water*V*g

FB=4.19*10^-3*1000*9.8

FB=41.06 N

c)

weight of the object air is,

w1=4.9 N

rho_object*V*g=4.9

rho_object*4.19*10^-3*9.8=4.9

===> rho_object = 119.33 kg/m^3

here,

density of the object is lessthan density of the water,

hence,

when the object is released it float to the surface

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