A frog in a hemispherical pod finds that he just floats without sinking in a flu

Question

A frog in a hemispherical pod finds that he just floats without sinking in a fluid of density 1.35 g/cm3. If the pod has a radius of 4.00 cm and negligible mass, what is the mass of the frog? (See Fig. P9.26.)
     kg

A small ferryboat is 4.00 m wide and 6.00 m long. When a loaded truck pulls onto it, the boat sinks an additional 4.10 cm into the water. What is the weight of the truck?
     N

                 A light spring of constant k = 170 N/m rests vertically on the bottom of a large beaker of water (Fig. P9.34a). A 5.95 kg block of wood (density = 650 kg/m3) is connected to the spring and the block-spring system is allowed to come to static equilibrium (Fig. P9.34b). What is the elongation, ?L, of the spring?
     cm

                 A thin spherical shell of mass 0.500 kg and diameter 0.240 m is filled with alcohol (? = 806 kg/m3). It is then released from rest at the bottom of a pool of water. Find the acceleration of the alcohol-filled shell as it starts to rise toward the surface of the water.
     m/s2

Explanation / Answer

1). let his mass be M

then graviatinal force= buyuant force

so Mg= d*V*g

or M=d*2/3*pi*r^3

where d is density so mass

= 180.064 gm

= 0.18Kg

2). wt of truck is M

so

Mg=dvg

or M= volume submerged*d

=4*6*0.041*1000

=984 Kg

3).balancing force we get

Mg= Kx+dV*g

now volume of wood= M/d

= 5.95/650

and density of water=1000 kg/m^3

so 5.95*9.8= (5.95/650)*1000+170*x

so x= 0.289 m

= 28.9 cm

4).total mass becomes 0.5+806*4/3*3.14*(0.12)^3

=6.33 kg

so net force= d*V*g-Mg

where d is density of water

so F=8.898

so a= F/M

= 1.4 m/s^2 upward

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