Q. Given, Force $= \frac{\alpha}{density + \ \beta^{3}}$ What are the dimensions of $\alpha,\beta?$
A) $\left\lbrack ML^{2}T^{- 2} \right\rbrack,\ \left\lbrack ML^{- 1/3} \right\rbrack$
B) $\left\lbrack M^{2}L^{4}T^{- 2} \right\rbrack,\ \left\lbrack M^{1/3}L^{- 1} \right\rbrack$
C) $\left\lbrack M^{2}L^{- 2}T^{- 2} \right\rbrack,\ \left\lbrack M^{1/3}L^{- 1} \right\rbrack$
D) $\left\lbrack M^{2}L^{- 2}T_{2} \right\rbrack,\ \left\lbrack {ML}^{- 3} \right\rbrack$
Explanation
Dimensions of $\beta^{3} = dimensions\ of\ density = \left\lbrack {ML}^{- 3} \right\rbrack$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \beta = \left\lbrack {M^{1/3}L}^{- 1} \right\rbrack$ Also $\alpha = force\ \times density$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left\lbrack {MLT}^{- 2} \right\rbrack\left\lbrack {ML}^{- 3} \right\rbrack$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left\lbrack M^{2}L^{- 2}T^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.