Question

. A pebble is dropped into water by a boy. He observes that ripples are formed
in water. Velocity of ripples formed depends on the density of water (p),

wavelength (a) and surface tension (T=F/l) Derive the formula for velocity
of ripples.
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Answer 1

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PHYSICS

The speed (v) of ripples on surface of water depends upon the surface tension (σ) density ρ and wave length (λ) the speed v is proportional to

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ANSWER

Let, v∝σ

a

ρ

b

λ

c

[M

0

LT

−1

]∝[MT

−2

]

a

[ML

−3

]

b

[L]

c

∝[ML]

a+b

[L]

−3b+c

[T]

−2a

equating the powers, we get,

a+b=0

−3b+c=1

−2a=−1

∴a=b=c=

2

1

∴v∝σ

2

1

ρ

−

2

1

λ

−

2

1

v∝

ρλ

σ