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A bullet is fired from a gun at the speed of $280\ \text{m s}^{-1}$ in the direction $30^\circ$ above the horizontal. The maximum height attained by the bullet is ($g = 9.8\ \text{m s}^{-2},\ \sin 30^\circ = 0.5$):
$H_{\max} = \dfrac{u^2 \sin^2\theta}{2g} = \dfrac{280^2 \times (0.5)^2}{2 \times 9.8} = 1000\ \text{m}$.
A metal wire has mass $(0.4 \pm 0.002)\ \text{g}$, radius $(0.3 \pm 0.001)\ \text{mm}$ and length $(5 \pm 0.02)\ \text{cm}$. The maximum possible percentage error in the measurement of density will nearly be:
$\dfrac{\Delta\rho}{\rho} = \dfrac{\Delta m}{m} + 2\dfrac{\Delta r}{r} + \dfrac{\Delta L}{L} = 0.5\% + 0.67\% + 0.4\% \approx 1.6\%$.
Given below are two statements:
Statement I: Photovoltaic devices can convert optical radiation into electricity.
Statement II: Zener diode is designed to operate under reverse bias in breakdown region.
In the light of the above statements, choose the most appropriate answer from the options given below:
Both statements describe standard properties of the respective semiconductor devices.
The magnetic energy stored in an inductor of inductance $4\ \mu\text{H}$ carrying a current of $2\ \text{A}$ is:
$U = \tfrac{1}{2} L I^2 = \tfrac{1}{2} (4 \times 10^{-6})(2)^2 = 8\ \mu\text{J}$.
If $\displaystyle \oint_S \vec{E} \cdot d\vec{S} = 0$ over a surface, then:
Zero net flux means inward and outward flux through the surface are equal (by Gauss's law, enclosed charge is zero).
The net magnetic flux through any closed surface is:
Magnetic monopoles do not exist; field lines form closed loops, so net flux through any closed surface is zero.
If the galvanometer $G$ does not show any deflection in the circuit shown, the value of $R$ is given by:
No deflection in $G$ means no current through it, so voltage across $R$ equals the 2 V cell EMF. Current in the outer loop = $(10-2)/400 = 0.02\ \text{A}$, hence $R = 2/0.02 = 100\ \Omega$.
In a series $LCR$ circuit, the inductance $L$ is $10\ \text{mH}$, capacitance $C$ is $1\ \mu\text{F}$ and resistance $R$ is $100\ \Omega$. The frequency at which resonance occurs is:
$f_0 = \dfrac{1}{2\pi\sqrt{LC}} = \dfrac{1}{2\pi\sqrt{10^{-2}\times 10^{-6}}} \approx 1.59\ \text{kHz}$.
The temperature of a gas is $-50^\circ\text{C}$. To what temperature the gas should be heated so that the rms speed is increased by 3 times?
$v_{rms}\propto\sqrt{T}$. "Increased by 3 times" $\Rightarrow v\to 4v$, so $T\to 16T$. $T_1 = 223\ \text{K}$, $T_2 = 16 \times 223 = 3568\ \text{K} = 3295^\circ\text{C}$.
Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of cross-sectional area $A$ of the wire is:
Tension throughout the wire equals $W$; stress = tension/area = $W/A$.
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The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.