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A constant voltage of 50 V is maintained between the points A and B of the circuit shown in the figure. The current through the branch CD of the circuit is:
With CD a connecting wire, $V_M = 32$ V. Current in $1\,\Omega$ (A→C) $= 18$ A and in $2\,\Omega$ (C→B) $= 16$ A, so $I_{CD} = 18-16 = 2.0$ A.
A photon and an electron (mass $m$) have the same energy $E$. The ratio $(\lambda_{\text{photon}}/\lambda_{\text{electron}})$ of their de Broglie wavelengths is: ($c$ is the speed of light)
$\lambda_{ph} = \dfrac{hc}{E}$, $\lambda_e = \dfrac{h}{\sqrt{2mE}}$. Ratio $= \dfrac{hc/E}{h/\sqrt{2mE}} = c\sqrt{\dfrac{2m}{E}}$.
Which of the following options represent the variation of photoelectric current with property of light shown on the x-axis?
Photoelectric (saturation) current is proportional to intensity (graph A) but is independent of frequency, so the current-vs-frequency graphs C and D are wrong. Only A is correct.
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is:
Taking mass $\propto r^3$: small sphere mass 1 unit, big 8 units. $I_{small} = \tfrac25 mR^2 + mR^2 = \tfrac75$ units; $I_{big} = \tfrac25(8)(2R)^2 = \tfrac{64}{5}$; $I_{rest} = \tfrac{57}{5}$. Ratio $= \dfrac{7}{57}$.
A full wave rectifier circuit with diodes $(D_1)$ and $(D_2)$ is shown in the figure. If input supply voltage $V_{in} = 220\sin(100\pi t)$ volt, then at $t = 15$ msec:
At $t = 15$ ms, $100\pi t = 1.5\pi$, $\sin(1.5\pi) = -1$, so $V_{in}$ is in its negative half cycle. Then $D_2$ conducts (forward biased) and $D_1$ is reverse biased.
Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas A and B are displaced by 16 cm and 9 cm, respectively. If the change in their internal energy is the same, then the ratio $r_A/r_B$ is equal to:
Same $Q$ and same $\Delta U\Rightarrow$ same $W = P\Delta V$. With equal $P$: $\pi r_A^2(16) = \pi r_B^2(9)\Rightarrow\dfrac{r_A}{r_B} = \sqrt{\dfrac{9}{16}} = \dfrac{3}{4}$.
A physical quantity $P$ is related to four observations $a$, $b$, $c$ and $d$ as follows: $P = \dfrac{a^3 b^2}{c\sqrt{d}}$. The percentage errors of measurement in $a$, $b$, $c$ and $d$ are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity $P$ is:
$\dfrac{\Delta P}{P} = 3(1\%) + 2(3\%) + 1(2\%) + \tfrac12(4\%) = 3+6+2+2 = 13\%$.
The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at $22.5^\circ$ from the polarization axis of one of the polaroid, is ($I_0$ is the intensity of polarised light after passing through the first polaroid):
$I = I_0\cos^2 22.5^\circ\cos^2 67.5^\circ = I_0\cos^2 22.5^\circ\sin^2 22.5^\circ = I_0\left(\tfrac12\sin45^\circ\right)^2 = \dfrac{I_0}{8}$.
Two identical point masses P and Q, suspended from two separate massless springs of spring constants $k_1$ and $k_2$, respectively, oscillate vertically. If their maximum speeds are the same, the ratio $(A_Q/A_P)$ of the amplitude $A_Q$ of mass Q to the amplitude $A_P$ of mass P is:
$v_{max} = A\omega = A\sqrt{k/m}$. Equal masses and equal $v_{max}$: $A_P\sqrt{k_1} = A_Q\sqrt{k_2}\Rightarrow\dfrac{A_Q}{A_P} = \sqrt{\dfrac{k_1}{k_2}}$.
A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:
Open pipe: $f = \dfrac{v}{2L}$. Half-submerged becomes a closed pipe of length $L/2$: $f' = \dfrac{v}{4(L/2)} = \dfrac{v}{2L} = f$.
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