A spherical steel ball of radius 0.05 m is suspended with the help of a string a

Question

A spherical steel ball of radius 0.05 m is suspended with the help of a string as shown. Consider the density of the steel 7800 kg/m3. The density of water is 1000 kg/m3. Use V = (4/3) ?R3 for the volume of a sphere where R is the radius of the sphere.

Fig A:

Find the tension in the string:
(a) If the ball is in the air as shown in the figure (a). (Ans: 40N)
(b) If the ball is completely immersed into the water as shown in the figure (b) (Ans: 35N)
(c) If half of the volume of the ball is dipped into the water as shown in the figure (c) (Ans: 37N)

A spherical steel ball of radius 0.05 m is suspended with the help of a string as shown. Consider the density of the steel 7800 kg/m3. The density of water is 1000 kg/m3. Use V = (4/3) ?R3 for the volume of a sphere where R is the radius of the sphere. Fig A: Find the tension in the string: If the ball is in the air as shown in the figure (a). (Ans: 40N) If the ball is completely immersed into the water as shown in the figure (b) (Ans: 35N) If half of the volume of the ball is dipped into the water as shown in the figure (c) (Ans: 37N)

Explanation / Answer

V = 4 x pi x 0.05^3 / 3    =5.236 x 10-4 m^3

a) T = Vdg =5.236 x 10-4 x 7800 x 9.8 = 40.02 N

b) T = V(7800 - 1000) g = 34.89 N

c) T = V.7800g/2 + V.(7800-1000) x g/2   = 37.45 N

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