Question

# A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity η. After some time, the velocity of the ball attains a constant value known as terminal velocity vT. The terminal velocity depends on (i) the mass of the ball m, (ii) η, (iii) r and (iv) acceleration due to gravity g. . Which of the following relations is dimensionally correct?

A
vTmgrη
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
vTηrmg
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
vTmgηr
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
vTηrmg
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C vT∝mgηrFirst, we check option (a) Substitute dimensions of each quantity in R.H.S. of option (a) [mgηr]=[M1][L1T−2][M1L−1T−1][L1] =[M0L1T−1] This is dimension of velocity, so option is dimensionally correct. Final answer: (a)

Suggest Corrections
0
Explore more