Q. The position of a particle moving on $x$-axis is given by $x(t)=A\sin t+B\cos^2t+Ct^2+D$, where $t$ is time. The dimension of $\frac{ABC}D$ is
A) $L^2T^{-2}$
B) $L^2$
C) $L$
D) $L^3\,T^{-2}$
Explanation
[Solution by Dr. Abubacker] Each term has the dimension of length: $[A]=[B]=[D]=L$ (the trigonometric arguments are dimensionless) and $[C]=LT^{-2}$. So $\frac{ABC}D=\frac{L\cdot L\cdot LT^{-2}}{L}=L^2T^{-2}$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.