Force is given by the expression, F = A cos(B | vedclass

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

Question

(A) In the expression $F = A \cos(Bx) + C \cos(Dt)$, the argument of the trigonometric function must be dimensionless. Therefore, the dimensions of $B

Vedclass · Accepted Answer

velocity

Vedclass · Answer

(A) In the expression $F = A \cos(Bx) + C \cos(Dt)$, the argument of the trigonometric function must be dimensionless. Therefore, the dimensions of $Bx$ and $Dt$ must be equal to the dimension of a constant (dimensionless). $[Bx] = [M^0 L^0 T^0] \implies [B] = [x^{-1}] = [L^{-1}]$. $[Dt] = [M^0 L^0 T^0] \implies [D] = [t^{-1}] = [T^{-1}]$. Now, we find the dimension of $\left(\frac{D}{B}\right)$: $\left[\frac{D}{B}\right] = \frac{[T^{-1}]}{[L^{-1}]} = [L T^{-1}]$. Since $[L T^{-1}]$ represents the dimension of velocity, the correct option is $A$.

Force is given by the expression, $F = A \cos(Bx) + C \cos(Dt)$, where $x$ is displacement and $t$ is time. The dimension of $\left(\frac{D}{B}\right)$ is the same as that of

Similar Questions

$A$ force is represented by $F = ax^2 + bt^{1/2}$,where $x$ is distance and $t$ is time. The dimensions of $b^2/a$ are:

The position of a body with acceleration '$a$' is given by $x = K{a^m}{t^n}$,where $t$ is time. Find the dimensions of $m$ and $n$.

$A$ new system of units is proposed in which the unit of mass is $\alpha \ kg$,the unit of length is $\beta \ m$,and the unit of time is $\gamma \ s$. How much will $5 \ J$ measure in this new system?

Planck's constant $h$,speed of light $c$,and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are):
$(A)$ $M \propto \sqrt{c}$
$(B)$ $M \propto \sqrt{G}$
$(C)$ $L \propto \sqrt{h}$
$(D)$ $L \propto \sqrt{G}$

The velocity $v$ (in $cm/sec$) of a particle is given in terms of time $t$ (in $sec$) by the relation $v = at + \frac{b}{t + c}$. The dimensions of $a, b,$ and $c$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module