Question

The time period of a soap bubble is T which depends on pressure P, density D and surface tension S. then relation for T is: a) T∝Pds b) T∝Pd⁻³/₂d¹/₂s c) T∝Pd⁻²s³/₂ d) T∝Pd²s¹/₃

Answer 1

Answer:

The time period of a soap bubble is T which depends on pressure P, density D and surface tension S. then relation for T is: a) T∝Pds b) ...

Answer 2

Answer:

The correct answer is Option B : $P^{\frac{-3}{2}} d^{\frac{1}{2}} S$

Explanation:

Firstly, we take the dimensions of the given data :

T$=[T]$

P $=[M^1L^{-1}T^{-2}]$

d$=[M^1L^{-3}]$

S$=[M^1T^{-2}]$

To find the relation for time period T :

Time periods ∝ Pressure

Time periods ∝ Density

Time periods ∝ Surface tension

T ∝ $P^ad^bS^c$

LHS and RHS must be dimensionally equal.

$[T^1]=[M^1L^{-1}T^{-2}][M^1L^{-3}][M^1T^{-2}]$

M ⇒ $0=a+b+c$

L ⇒ $0=-a-3b$     --- This can be written as $a=-3b$

T ⇒ $1=-2a-2c$

L ⇒ $0=-3b+b+c$

$0=-2b+c\\c=2b$

T ⇒ $1=-2(-3b)-2(2b)$

$1=6b-4b\\b=\frac{1}{2}$

From the value of b, we get :

$a=\frac{-3}{2}\\ c=1$

T ∝ $P^ad^bS^c$

T ∝ $P^{\frac{-3}{2}} d^{\frac{1}{2}} S^1$

Hence we get the relation.