If the time period T propto P^a d^b E^c,where | vedclass

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

Question

(C) The dimensional formula for time period $T$ is $[M^0 L^0 T^1]$.The dimensional formulas for the given physical quantities are:Pressure $P = [M L^{

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(C) The dimensional formula for time period $T$ is $[M^0 L^0 T^1]$.The dimensional formulas for the given physical quantities are:Pressure $P = [M L^{-1} T^{-2}]$Density $d = [M L^{-3}]$Energy $E = [M L^2 T^{-2}]$Given the relation $T = k P^a d^b E^c$,we write the dimensional equation:$[M^0 L^0 T^1] = [M L^{-1} T^{-2}]^a [M L^{-3}]^b [M L^2 T^{-2}]^c$$[M^0 L^0 T^1] = M^{a+b+c} L^{-a-3b+2c} T^{-2a-2c}$Comparing the powers of $M, L,$ and $T$ on both sides:$1$) $a + b + c = 0$$2$) $-a - 3b + 2c = 0$$3$) $-2a - 2c = 1$From equation $(3)$,$-2(a + c) = 1$,so $a + c = -1/2$.Substitute $a + c = -1/2$ into equation $(1)$: $(-1/2) + b = 0$,which gives $b = 1/2$.Substitute $b = 1/2$ into equation $(2)$: $-a - 3(1/2) + 2c = 0 \Rightarrow -a + 2c = 3/2$.Now we have a system of two equations:$a + c = -1/2$$-a + 2c = 3/2$Adding these two equations: $3c = 1$,so $c = 1/3$.

If the time period $T \propto P^a d^b E^c$,where $P$ is pressure,$d$ is density,and $E$ is energy,then the value of $c$ is:

Similar Questions

The speed of ripples $(v)$ on a water surface depends on surface tension $(\sigma)$,density $(\rho)$,and wavelength $(\lambda)$. Then the square of speed $(v^2)$ is proportional to

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a \sin(ct) + b \cos(dx)$. Then the dimension of $a/b$ is:

Show that $\frac{\text{Joule}}{\text{meter}^2} = \frac{\text{Newton}}{\text{meter}}$.

$A$ quantity $f$ is given by $f = \sqrt{\frac{hc^5}{G}}$,where $c$ is the speed of light,$G$ is the universal gravitational constant,and $h$ is Planck's constant. The dimension of $f$ is that of:

With the usual notations,the following equation $S_t = u + \frac{1}{2}a(2t - 1)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module