JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
A ball of radius r and density \(\rho\) dropped through a viscous liquid of density \(\sigma\) and viscosity \(\eta\) attains its terminal velocity at time t , given by \(t = A \rho^{ a } r ^{ b } \eta^{ c } \sigma^{ d }\), where A is a constant and a , b c and d are integers. The value of \(\frac{b+c}{a+d}\) is ___________.
- A 1
- B 2
- C -1
- D 0
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(T=\left(ML^{-3}\right)^{a} L^{b}\left(ML^{-1} T^{-1}\right)^{c}\left(ML^{-3}\right)^{d}\) \(T = M ^{ a + cd d} L^{-3 a - c - adb } T ^{- c }\) on comparing \(c =-1 ; a + c + d =0 ;-3 a - c -3 d+ b =0\) \(b =2 ; a + d =1\) \(b+c=1\)
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