Agraduated cylinder is filled to the 40.00-ml mark with a mineral oil. the masses of the cylinder before and after the addition of the mineral oil are 124.966 g and 159.446 g, respectively. in a separate experiment, a metal ball bearing of mass 18.713 g is placed in the cylinder and the cylinder is again filled to the 40.00-ml mark with the mineral oil. the combined mass of the ball bearing and mineral oil is 50.952 g. calculate the density and radius of the ball bearing (volume of a sphere of radius r is 4/3ïr^3

Firstly, Let's experiment this !

Experiment 1 :

159.446g - 124.966g = 34.48g

34.48g = The mass of Mineral oil.

The density of the mineral oil = M/V = 34.48g/40mL = 0.862g/cm³.

Experiment 2 :

124.966 + 18.173 = 143.139 = The mass of solid + cylinder.

124.966 + 50.952 = 175.918 = The mass of solid + cylinder + Mineral water.

175.918 - 143.139 = 32.779 = The mass of added mineral oil.

Explanation:

Now we have to find the volume of the added mineral oil using the density from experiment 1.

V = 32.779g/0.862g/cm³ = 38.02668213mL

Since we found the volume of the solid, we then have to subtract the added mineral oil volume from the total volume from experiment 1.

Volume of solid = 40-38.02668213 = 1.97331787mL

Density of solid = 18.713g/1.97331787mL = 9.483013499g/cm^3

1.97331787 = (4/3)(3.14)r³

1.97331787*(3/4)(3.14) = .4713338861

.4713338861 = r ³

r = 0.7782328425158433

r = 0.78

Now that's our final answer ! r = 0.78

when the volume of gas is   changed from   717.73 ml   to 852 ml   the temperature will   change   from 315   c to 452   c

    calculation

this is calculated using the charles law formula

that is,   v1/t1 = v2/t2

          v1=?

        t1 = 315 c   into   kelvin = 315 +273 = 588 k

        v2 = 852   ml

        t2 = 425c + 273 =698 k

make v1   the subject of the formula ( by   multiplying both side by t1)

  v1=( v2 xt1) / t2

v1= (852 ml   x 588 k)/ 698 k= 717.73 ml