Frequency is the function of density (ρ), length (a) and surface tension (T). Then its value is (k is a constant)
A
kρ−1/2a−3/2T1/2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
kρ1/2a3/2T−1/2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
kρ1/2a−3/2T1/2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
kρ−1/2a3/2T−1/2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Akρ−1/2a−3/2T1/2 Frequency (n)=kρaabTc,k= constant
Where density (ρ)=Massvolume =[M][L3]=[M1L−3] a= length =[L1]
Surface Tension (T)=Forcelength =M1L1T−2L1=[M1T−2] ∵ Frequency =1time=[T−1]
Now from equation (1) [T−1]=[M1L−3]a[L1]b[M1T−2]c [M0L0T−1]=[Ma+cL−3a+bT−2c]
Comparing the powers of LHS and RHS 0=a+c⇒c=−a ... (1) −3a+b=0 ... (2) −2c=−1⇒c=12 ... (3) ∴ From equation (1) and (3) a=−12
Now from equation (2) −3(−12)+b=0 b=−32 b=−32
Now substituting the value of a,b and c in equation (1) n=kρ−1/2a−3/2T1/2