The velocity v (in cm/sec) of a particle is g | vedclass

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

Question

(C) According to the principle of dimensional homogeneity,the dimensions of each term in an equation must be the same.$1$. For the term $c$: Since $c$

Vedclass · Accepted Answer

$a = LT^{-2}, b = L, c = T$

Vedclass · Answer

(C) According to the principle of dimensional homogeneity,the dimensions of each term in an equation must be the same.$1$. For the term $c$: Since $c$ is added to $t$ (time),the dimension of $c$ must be the same as the dimension of $t$. Therefore,$[c] = [T]$.$2$. For the term $at$: The dimension of $at$ must be equal to the dimension of velocity $v$. Thus,$[a][T] = [LT^{-1}]$,which gives $[a] = [LT^{-2}]$.$3$. For the term $\frac{b}{t+c}$: The dimension of the entire term must be equal to the dimension of velocity $v$. Since $[t+c] = [T]$,we have $\frac{[b]}{[T]} = [LT^{-1}]$. Therefore,$[b] = [L]$.Thus,the dimensions are $a = LT^{-2}, b = L, c = T$.

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:

Similar Questions

Consider the equation $\frac{1}{2} m v^{2} = m g h$,where $m$ is the mass of the body,$v$ is the velocity,$g$ is the acceleration due to gravity,and $h$ is the height. Is this equation dimensionally correct?

If speed of light in vacuum $\left(3 \times 10^8 \,m/s\right)$, acceleration due to gravity $\left(10 \,m/s^2\right)$ and mass of electron $\left(9.1 \times 10^{-31} \,kg\right)$ are taken as fundamental physical quantities, then the unit of time in this system is

The equation of a wave is given by $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,where $\omega$ is the angular velocity and $v$ is the linear velocity. The dimension of $k$ is

If mass is written as $m=kc^{p} G^{-1 / 2} \,h^{1 / 2}$ then the value of $P$ will be : (Constants have their usual meaning with $k$ a dimensionless constant)

If the unit of force is $100\,N$,unit of length is $10\,m$ and unit of time is $100\,s$,what is the unit of mass in this system of units?

Vedclass Test Series

Exam Paper Generator

Online Exam Module