10.3 Solutions
455
Breaking stress = maximum stretching force/area
=
L Aρg
A
= Lρg
7.8 × 10
8
= L × 7800 × 9.8
∴ L = 1.021 × 10
4 m = 10.2 km
Note that the result is independent of cross-sectional area of the wire.
10.3.7 Surface Tension
10.62 S =
h +
r
3
rρg
2 cos θ
Assuming that the contact angle θ = 0
h =
2s
r ρg
−
r
3
=
2 × 0.072
10 −3 × 10 3 × 9.8
−
10 −3
3
= 0.01436 m
= 1.436 cm
10.63 Pressure due to water column of depth h is
P = hgρ
Total pressure of the bubble, ignoring surface tension,
P
= P + P 0 = hgρ + P 0
= 100 × 9.8 × 1000 + 1.01 × 10
5
= 10.81 × 10
5
P
V = nRT
∴ V =
nRT
P =
1 × 8.314 × 293
10.81 × 10 5 = 2.25 × 10
−3 m
3
10.64 As the drops are incompressible, the volume is constant.
n
4
3
πr
3
=
4π
3
R
3
∴ R = rn
1/3
Decrease in surface area = 4πr 2 n − 4π R 2 = 4πr 2
n − n 2/3
Energy released = (decrease in surface area) (surface tension)