Given: Force =(α/ text density +β3) What are the dimensions of α, β ?

Question

Given: Force =(α/ text density +β3) What are the dimensions of α, β ? (A) ML -2 T -2, ML -1 / 3 (B) M2 L4 T-2, M-1 / 3 L-1 (C) M2 L-2 T-2, M1 / 3 L-1 (D) M2 L-2 T-2, M L-3

Tardigrade Admin · Accepted Answer

β3= density =M1 L-3 β=M1 / 2 L-1 Also; α= force × density =ML T-2 × M1 L-3 = MLT -2 × M 1 L -3=[ M 2 L -2 T -2]

Q. Given: Force $= \frac{α}{density + β ^{3}}$ What are the dimensions of $α, β$ ?

$M L^{- 2} T^{- 2}, M L^{- 1/3}$

$M^{2} L^{4} T^{- 2}, M^{- 1/3} L^{- 1}$

$M^{2} L^{- 2} T^{- 2}, M^{1/3} L^{- 1}$

$M^{2} L^{- 2} T^{- 2}, M L^{- 3}$

$β^{3} =$ density $= M^{1} L^{- 3}$
$β = M^{1/2} L^{- 1}$
Also; $α =$ force $\times$ density
$= M L T^{- 2} \times M^{1} L^{- 3}$
$= M L T^{- 2} \times M^{1} L^{- 3} = [M^{2} L^{- 2} T^{- 2}]$

Q. Given: Force = density +β3α​ What are the dimensions of α,β ?

ML−2T−2,ML−1/3

M2L4T−2,M−1/3L−1

M2L−2T−2,M1/3L−1

M2L−2T−2,ML−3