Home
Class 12
PHYSICS
If the time period (T)of vibration of a ...

If the time period `(T)`of vibration of a liquid drop depends on surface tension `(S)` , radius`( r )` of the drop , and density `( rho )` of the liquid , then find the expression of `T`.

A

`T = k sqrt((r^3 rho)/(S))`

B

`T = k sqrt((Srho)/(r^3))`

C

`T = k sqrt((r^3 )/(S rho))`

D

`T = k sqrt((r^3 S)/(rho))`

Text Solution

Verified by Experts

The correct Answer is:
A
We can say `T = k(S)^a (r)^b (rho)^c implies [T] = [MT^(-2)]^(a) [L]^(b)[ML^(-3)]^(c)`
We can say `a + c = 0`
`b - 3c = 0`
`- 2a = 1`
So, `a = 1/2 , c = + 1/2 & b = +3/2`
So `T = k (S)^(-1//2)(r)^(3//2)(rho)^(1//2) or T = k sqrt((r^3 rho)/(S))`
Promotional Banner

Similar Questions

Explore conceptually related problems

The time period (t) of vibration of a liquid drop depends on surface tension (s),radius ( r) of the drop and density (rho) of the liquid .Find t.

The time period (T) of small oscillations of the surface of a liquid drop depends on its surface tension (s), the density (rho) of the liquid and it's mean radius (r) as T = cs^(x) rho^(y)r^(z) . If in the measurement of the mean radius of the drop, the error is 2 % , the error in the measurement of surface tension and density both are of 1% . Find the percentage error in measurement of the time period.

A spherical liquid drop is placed on a horizontal plane . A small distrubance cause the volume of the drop to oscillate . The time period oscillation (T) of the liquid drop depends on radius (r) of the drop , density (rho) and surface tension tension (S) of the liquid. Which amount the following will be be a possible expression for T (where k is a dimensionless constant)?

Internal pressure inside a liquid drop of radius r and surface tension T is

The excess pressure inside the drop of a liquid of surface tension T and radius of drom r is

If the velcoity of surface wave (v) depends upon surface tension (T), coefficient of visosity (eta) and density (rho) then the expression for v will be .

Eight spherical droplets, each of radius r of a liquid of density rho and surface ternsion T coalesce to form one big drop. If s is the specific heat of the liquid then the rise in the temperature of the liquid in this process is

The excess pressure in dyne/ inside a liquid drop of radius 2 mm and fsurface tension T is