Q 11-01-186JEE MainJEE Main 2021 (25 Jul, Shift 2)Easy
The force is given in terms of time $t$ and displacement $x$ by the equation $F = A\cos Bx + C\sin Dt$. The dimensional formula of $\frac{AD}{B}$ is:
Answer: (B) $[\text{ML}^2\text{T}^{-3}]$
$A$ has the dimensions of force: $[\text{MLT}^{-2}]$.
$Bx$ and $Dt$ are dimensionless: $[B] = [\text{L}^{-1}]$, $[D] = [\text{T}^{-1}]$.
$$\left[\frac{AD}{B}\right] = \frac{[\text{MLT}^{-2}][\text{T}^{-1}]}{[\text{L}^{-1}]} = [\text{ML}^2\text{T}^{-3}]$$
Solution by Sreeraj P, M.Sc Physics