Let force F = A sin(Ct) + B cos(Dx),where x a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The argument of a trigonometric function must be dimensionless. Given $F = A \sin(Ct) + B \cos(Dx)$. For the term $\sin(Ct)$,the argument $Ct$ mus

Vedclass · Accepted Answer

velocity

Vedclass · Answer

(D) The argument of a trigonometric function must be dimensionless. Given $F = A \sin(Ct) + B \cos(Dx)$. For the term $\sin(Ct)$,the argument $Ct$ must be dimensionless. $[Ct] = [M^0 L^0 T^0] \implies [C][T] = [T^0] \implies [C] = [T^{-1}]$. For the term $\cos(Dx)$,the argument $Dx$ must be dimensionless. $[Dx] = [M^0 L^0 T^0] \implies [D][L] = [L^0] \implies [D] = [L^{-1}]$. Now,the dimensions of $\frac{C}{D}$ are: $\left[ \frac{C}{D} \right] = \frac{[T^{-1}]}{[L^{-1}]} = [L T^{-1}]$. These are the dimensions of velocity. Therefore,the correct option is $D$.

Let force $F = A \sin(Ct) + B \cos(Dx)$,where $x$ and $t$ are displacement and time respectively. The dimensions of $\frac{C}{D}$ are the same as the dimensions of

Similar Questions

If energy $(E)$,velocity $(v)$,and force $(F)$ are taken as fundamental quantities,what are the dimensions of mass?

Which one of the following combinations of constants has the dimensions of time? $[G=$ gravitational constant,$h=$ Planck's constant,$c=$ velocity of light$]$

If the units of force,energy,and velocity are respectively $10\, N$,$100\, J$,and $5\, m/s$,then the units of length,mass,and time will be:

If force $(F)$,velocity $(V)$,and time $(T)$ are taken as fundamental units,then the dimensions of mass are:

Heat produced in a current-carrying conducting wire depends on current $I$,resistance $R$ of the wire,and time $t$ for which the current is passed. Using these facts,obtain the formula for heat energy.

Vedclass Test Series

Exam Paper Generator

Online Exam Module