Which equation is dimensionally incorrect? [Here, t= Time, p = Momentum, i = Impuls, m = Mass, g = Acceleration, v = Speed, f= Force, r = radius/distance, I= Industance, C = Capacitance, R = Resistance, I = Moment of inertia)

Question

Which equation is dimensionally incorrect? [Here, t= Time, p = Momentum, i = Impuls, m = Mass, g = Acceleration, v = Speed, f= Force, r = radius/distance, I= Industance, C = Capacitance, R = Resistance, I = Moment of inertia) (A) i=p + mgt (B) t = (mv2/2) + Fr (C) mvr = Iω + Fr (D) (L/R)=RC+(r/(1 /√μ0ε0))

Tardigrade Admin · Accepted Answer

mvr and Iω have same dimensions, i.e., [ML2T-1] while Fr has dimensions [ML2T-2].

Q. Which equation is dimensionally incorrect?
[Here, $t =$ Time, $p =$ Momentum, $i =$ Impuls, $m =$ Mass, $g =$ Acceleration, $v =$ Speed, $f =$ Force, $r =$ radius/distance, $I =$ Industance, $C =$ Capacitance, $R =$ Resistance, $I =$ Moment of inertia)

$i = p + m g t$

$t = (m v^{2} /2) + F r$

$m v r = I ω + F r$

$\frac{L}{R} = RC + \frac{r}{( 1/ μ _{0} ε _{0} )}$

$m v r$ and $I ω$ have same dimensions, i.e., $[M L^{2} T^{- 1}]$ while $F r$ has dimensions $[M L^{2} T^{- 2}]$ .

Q. Which equation is dimensionally incorrect? [Here, t= Time, p= Momentum, i= Impuls, m= Mass, g= Acceleration, v= Speed, f= Force, r= radius/distance, I= Industance, C= Capacitance, R= Resistance, I= Moment of inertia)

i=p+mgt

t=(mv2/2)+Fr

mvr=Iω+Fr

RL​=RC+(1/μ0​ε0​​)r​