A cylindrical metallic rod,in thermal contact | vedclass

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

Question

(C) The rate of heat flow through a rod is given by $\frac{Q}{t} = \frac{kA(T_1 - T_2)}{\ell}$.Since the volume $V = A\ell$ is constant,we can write $

Vedclass · Accepted Answer

$\frac{Q}{16}$

Vedclass · Answer

(C) The rate of heat flow through a rod is given by $\frac{Q}{t} = \frac{kA(T_1 - T_2)}{\ell}$.Since the volume $V = A\ell$ is constant,we can write $\ell = \frac{V}{A}$.Substituting this into the equation: $\frac{Q}{t} = \frac{kA(T_1 - T_2)}{V/A} = \frac{kA^2(T_1 - T_2)}{V}$.Since $k, T_1, T_2,$ and $V$ are constant,we have $Q \propto A^2$.Given that the radius $r_2 = \frac{r_1}{2}$,the area $A = \pi r^2$ implies $A_2 = \pi (r_1/2)^2 = \frac{A_1}{4}$.Therefore,$\frac{Q_2}{Q_1} = \left(\frac{A_2}{A_1}\right)^2 = \left(\frac{1}{4}\right)^2 = \frac{1}{16}$.Thus,$Q_2 = \frac{Q}{16}$.

Similar Questions

The bonds present in ${N_2}{O_5}$ are ........

$\frac{\sqrt{8+\sqrt{28}}+\sqrt{8-\sqrt{28}}}{\sqrt{8+\sqrt{28}}-\sqrt{8-\sqrt{28}}}$ is equal to

Which of the following factors increase the heart rate?
$(a)$ Sympathetic nerve signals
$(b)$ Parasympathetic nerve signals
$(c)$ Adrenal medullary hormones
$(d)$ Vagus nerve
$(e)$ Thyroxine hormone
$(f)$ Acetylcholine

From the following thermochemical equations,find out the heat of ionisation $Z$ for a weak acid $HA$:
$HA \to A^{-} + H^{+}$,$\Delta H = Z$
$H^{+} + OH^{-} \to H_2O$,$\Delta H = X$
$HA + OH^{-} \to A^{-} + H_2O$,$\Delta H = Y$

In the circuit shown,the reading of the Ammeter is doubled after the switch is closed. Each resistor has a resistance $1\,\Omega$ and the ideal cell has an $e.m.f.$ $10\,V$. Then,the Ammeter has a coil resistance equal to ............... $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module