Explore topic-wise InterviewSolutions in Current Affairs.

One mole of monatomic ideal gas is contained in a rigid container of volume $V$ with walls of total surface area $A$, thickness $x$ and thermal conductivity $K$. The gas is at an initial temperature $T_o$ and pressure $P_o$. The temperature of the surrounding air is $T_s$. All the temperatures are in absolute scale. If the temperature of the gas at any time $t$ can be expressed as $T\left(t\right)=T_s-(T_s-T_o)e^{-\lambda t}$, find the value of $\lambda$.

A box $\text{P}$ and a coil $\text{Q}$ are connected in series with an $AC$ source of variable frequency. The EMF of the source is constant at $10\text{V}$. Box $\text{P}$ contains a capacitance of $1\mu \text{F}$ in series with a resistance of $32\Omega$. Coil $\text{Q}$ has a self inductance of $4.9\text{mH}$ and a resistance of $68\Omega$. The frequency is adjusted so that the maximum current flows in $\text{P}$ and $\text{Q}$. If $Z_P$ and $Z_Q$ represents the impedance of box $\text{P}$ and $\text{Q}$ respectively, then

Find the tension $T_1$ in the string. All surfaces are smooth.

Derive an expression for time period of simple pendulum ( for 5marks question)

Given $\overrightarrow{C}=\overrightarrow{A}\times \overrightarrow{B}$ and $\overrightarrow{D}=\overrightarrow{B}\times \overrightarrow{A}$, Then the angle between $\overrightarrow{C}$and $\overrightarrow{D}$ is.

A ball of mass m moving horizontally at a speed v collides with the bob of a simple pendulum at rest. The mass of the bob is also m, if the collision is perfectly elastic, the bob of the pendulum will rise to a height of

A bullet of mass $200\text{g}$ fired with a velocity of $200\text{m/s}$, hits a block of mass $2\text{kg}$ moving with a velocity of $10\text{m/s}$. After hitting the block, the bullet lodges into it. What is the velocity of the combined system? Assume that the collision is perfectly inelastic.

An oil engine working on dual engine cycle takes air at 1.0 bar and ${16}^{\circ }C$. The maximum cycle pressure is 60 bar. The compression ratio is 14:1. The heat addition at constant pressures equal to heat addition at constant volume. What is the air standard efficiency of the cycle?

A soap bubble of radius $r$ is in vaccum. The number of moles of gas trapped in the soap bubble is proportional to

An iron rod of length $50\text{cm}$ is joined at an end to an aluminium rod of equal length to form a system. All measurements refer to ${20}^{\circ }C$. If coefficient of linear expansion of iron and aluminium are $12\times {10}^{-6}{/}^{\circ }C$ and $24\times {10}^{-6}{/}^{\circ }C$ respectively, find average coefficient of linear expansion of composite system?

1. 0.943

Assume that light of wavelength $600\text{nm}$ is coming from a star. The limit of resolution of telescope whose objective has a diameter of $2\text{m}$ is

A gramophone record of mass $M$ and radius $R$ is rotating at an angular velocity $\omega$. A coin of mass $m$ is gently placed on the record at a distance $r=R/2$ from its centre. The new angular velocity of the system is

In the circuit shown, each capacitor has a capacitance C. The emf of the cell is E. If the switch S is closed, the amount heat loss is

A ring of mass $M$ and radius $R$ lies in the $x-y$ plane with its centre at the origin as shown. The mass distribution of the ring is non-uniform such that at any point $\text{P}$ on the ring, the mass per unit length is given by $\lambda ={\lambda }_0{\cos }^2\theta$ (where ${\lambda }_0$ is a positive constant). Then the moment of inertia of the ring about $z-$ axis is:

The magnetic induction field strength at a distance of $0.3\text{m}$ on the axial line of a short bar magnet of moment $3.6{\text{Am}}^2$ is

If the electron has same momentum as that of a photon of wavelength $5200\stackrel{\circ }{A}$, then the velocity of electron in m /sec is given by

In adjoining LCR circuit, reading of which voltmeter will be zero at resonance condition ?

Using dimensional analysis, find the value of $x$ in the relation, $Y=\frac{T^x.\cos \theta .\tau }{L^3}$ where, $Y$ is Young's Modulus, $T$ is the time period, $\tau$ is torque and $L$ is length.

Length of the minute hand in a clock is $10\text{cm}$. Find difference between average speed and magnitude of average velocity (in $cm/min$) of tip of the minute hand from $6$ a.m. to $6:20$ a.m.

A long solenoid of $50\text{cm}$ length having $100$ turns carries a current of $2.5\text{A}$. The magnetic field at the centre of the solenoid is :

$({\mu }_o=4\pi \times {10}^{-7}{\text{Tm A}}^{-1})$

A ball of mass $1\text{kg}$ is attached to an inextensible string. The ball is released from the position shown in figure. Find the magnitude of impulse imparted by the string to the ball immediately after the string becomes taut. Take $g=10{\text{m/s}}^2$.

In the given figure, the coefficient of friction between the two blocks is $\mu$, and all other surfaces are smooth. Find the minimum value of $F$ which will prevent slipping.

In the figure shown, the wires $\text{AB}$ and $\text{PQ}$ carry steady currents, $I_1$ and $I_2$ respectively. $\text{PQ}$ is of uniformly distributed mass $m$ and length $l$. $\text{AB}$ and $\text{PQ}$ are both horizontal and kept in the same vertical plane. The $\text{PQ}$ is in equilibrium at height $h$. Find $h$ in terms of $I_1,I_2,l,m$ and other standard constants.