The time period T of vibration of a liquid drop depends on surface tension S radius r of drop and density d of the liquid Find a relation for T
Answers
Hey mate,.
Time of oscillation,
t α p^a α r^k α σ^c
So, t = k(p^a)(r^k)(σ^c)
Writing dimensions of both sides,
[T] = [ML^-3]^a [L]^b [MT^-2]^c
= [M^(a+c) L^(-3a+b) T^(-2c)]
Comparing powers of M,L and T on both sides, we have
a + c = 0 …(i)
-3a + b = 0 …(ii)
-2c = 1 …(iii)
Solving eqs (i), (ii) and (iii), we get,
a = 1/2, c= -1/2, b = 3/2
Putting the values in t
t = k(p^1/2)(r^3/2)(σ^-1/2)
t α √[(pr^3)/σ]
Hope it will help you
Answer:
Time of oscillation,
t α p^a α r^k α σ^c
So, t = k(p^a)(r^k)(σ^c)
Writing dimensions of both sides,
[T] = [ML^-3]^a [L]^b [MT^-2]^c
= [M^(a+c) L^(-3a+b) T^(-2c)]
Comparing powers of M,L and T on both sides, we have
a + c = 0 …(i)
-3a + b = 0 …(ii)
-2c = 1 …(iii)
Solving eqs (i), (ii) and (iii), we get,
a = 1/2, c= -1/2, b = 3/2
Putting the values in t
t = k(p^1/2)(r^3/2)(σ^-1/2)
t α √[(pr^3)/σ]