Q. Position of a body with acceleration $a$ is given by $x = ka^{m}\ t^{n}.$ Here $t$ is time. Find the dimensions of $m\ and\ n.$
A) $m = 1,\ n = 1$
B) $m = 1,\ n = 2$
C) $m = 2,\ n = 1\$
D) $m = 2,\ n = 2\$
Explanation
Positions $x = ka^{m}t^{n}$ $\ \ \ \ \ \left\lbrack M^{0}LT^{0} \right\rbrack = \left\lbrack LT^{- 2} \right\rbrack^{m}\lbrack T\rbrack^{n}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \left\lbrack M^{0}L^{m}T^{- 2m + n} \right\rbrack$ On comparing both sides $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ m = 1$ $\ \ \ \ - 2m + n = 0$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n = 2m$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n = 2 \times 1 = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.