JEE 2016 :: Advanced 2016 :: Physics 2016

• Advanced 2016 - Physics 2016
• Advanced 2016 - Chemistry 2016
• Advanced 2016 - Mathematics 2016

Consider two solid spheres P and Q each of density 8 gm cm^-3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm^-3 and viscosity η = 3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm^-3 and viscosity η = 2 poiseulles. The ratio of the terminal velocities of P and Q is

Answer:

Explanation:

Terminal velocity is given by 

$v_{T}=\frac{2}{9}\frac{r^{2}}{\eta}(d-\rho)g$

$v_{T}=\frac{2}{9}\frac{r^{2}}{\eta}(d-\rho)g$

$\left(\frac{1}{0.5}\right)^{2}\times \left(\frac{2}{3}\right)\times \frac{(8-.08)}{(8-1.6)}=4\times \frac{2}{3}\times \frac{7.2}{6.4}=3$

Two inductors  L₁ (inductance lmH, internal resistance 3Ω) and k (inductance 2 mH, internal resistance 4 Ω), and a resistor R (resistance 12 Ω) are all connected in parallel across a 5V battery. The circuit is switched on at time t = 0. The ratio of the maximum to the minimum current (I_max , I_min ) drawn from the battery is

Answer:

Explanation:

$I_{max}=\frac{\epsilon}{R}=\frac{5}{12}A$

(Initially t=0)

$I_{min}=\frac{\epsilon}{R_{eq}}=\epsilon \left(\frac{1}{r_{1}}+\frac{1}{r_{2}}+\frac{1}{R}\right)$

(finally in steady state)

$=5\left(\frac{1}{3}+\frac{1}{4}+\frac{1}{12}\right)=\frac{10}{3}A$

$\frac{I_{max}}{I_{min}}=8$

 A hydrogen atom in its ground state is irradiated by light of wavelength 970Å. Taking $hc/e =1.237\times 10^{-6} eVm$ and the ground state energy of hydrogen atom as - 13.6 eV the number of lines present in the emission spectrum is

Answer:

Explanation:

Energy of incident light (in eV) $E=\frac{12375}{970}=12.7 eV$

After excitation, let the electron jumps to nth State ,then $\frac{-13.6}{n^{2}}=-13.6+12.7$

Solving this equation, we get n=4;

Total number of lines in emission spectrum ,$ =  \frac{n(n-1)}{2}=\frac{4(4-1)}{2}=6$

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. lf the bulb is powered at constant voltage, which of the following statement(s) is (are) true?

Answer:

Explanation:

Because of non-uniform evaporation at different section, area of cross-section would be different at different sections. Region of highest evaporation rate would have rapidly reduced area and would become break up cross-section.

Resistance of the wire as whole increases with time. Overall resistance increases hence power decreases.

$\left(p=\frac{V^{2}}{R } , P\propto \frac{1}{R} \right)$ as V  is constant.

At break up junction temperature would be highest, thus light of highest band frequency would be emitted at those cross-section.

Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principle quantum number n. where n >>1. Which of the following statement(s) is (are) true?

Answer:

Explanation:

As radius,

$r\propto \frac{n}{z}$

$\Rightarrow \frac{\delta r}{r}=\frac{\left(\frac{n+1}{z}\right)^{2}-\left(\frac{n}{z}\right)^{2}}{\left(\frac{n}{z}\right)^{2}}$

$\frac{2n+1}{n^{2}\approx \frac{2}{n}\propto \frac{1}{n}}$

Energy $E\propto \frac{z^{2}}{n^{2}}$

$\Rightarrow \frac{\triangle E}{E}=\frac{\frac{z^{2}}{n^{2}}-\frac{z^{2}}{(n+1)^{2}}}{\frac{z^{2}}{(n+1)^{2}}}$

$=\frac{n+1^{2}-n^{2}}{n^{2}.(n+1)^{2}}.(n+1)^{2}$

$\Rightarrow \frac{\triangle E}{E}=\frac{2n+1}{n^{2}}\simeq \frac{2n}{n^{2}}\propto \frac{1}{n}$

Angular momentum $L=\frac{nh}{2\pi}$

$\Rightarrow \frac{\triangle L}{L}=\frac{\frac{(n+1)h}{2\pi}-\frac{nh}{2\pi}}{\frac{nh}{2\pi}}$

$=\frac{1}{n} \propto \frac{1}{n}$

• Advanced 2016 - Physics 2016
• Advanced 2016 - Chemistry 2016
• Advanced 2016 - Mathematics 2016