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The figure shows the face and interface temperature of a composite slab consisting of four materials, of identical thickness, through which the heat transfer is steady. Which material has minimum thermal conductivity?

A block kept on a rough inclined plane as shown in the figure, remains at rest upto a maximum force $2N$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10N$. The coefficient of static friction between the block and the plane is
[Take $g=10m/s^2]$

The ${\epsilon }_0$ and ${\mu }_0$ are the electric pemittivity and magnetic permeability in a free space. If $\epsilon$ and ${\mu }^{}$ are the corresponding quantities in medium, the refractive index of the medium is

A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0, (6m, 7m) at t = 2 sec and (13m, 14m) at time t = 5 sec. Average velocity vector $V_{avg}$ from t = 0 to t = 5 sec is:

A light source lies at the angle bisector of two plane mirrors inclined at an angle of $\theta$. The limitation for the value of $\theta$ so that the light reflected from one mirror does not reach the other mirror will be

The third harmonic of a closed organ pipe is equal to the second overtone of an open organ pipe. If the length of open organ pipe is $60\text{cm}$, then the length of closed organ pipe will be

If $\overrightarrow{A}=3\hat{i}+4\hat{j}$, $\overrightarrow{B}=\sqrt{3}\hat{i}-\hat{j}$ and angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${30}^{\circ }$. Find $|\overrightarrow{A}\times \overrightarrow{B}|$

The friction coefficient between the two blocks shown in figure is $\mu$ but the floor is smooth. Assume the entire system is kept inside an elevator coming down with an acceleration a < g.

Two wires are made of the same material and have the same volume. However wire $1$ has cross-sectional area $A$ and wire $2$ has cross-sectional area $3$A. If the length of wire $1$ increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire $2$ by the same amount?

The ratio of kinetic energy of two bodies is $2:1$ and their angular momentum are in the ratio of $1:2$. Then the ratio of their moment of inertia will be (assume pure rotational motion)

In the same example, if the volume increased from $1.6385\times {10}^{-3}{m}^{3}to2.1385\times {10}^{-3}{m}^3$, how much work would be done by the gas?

Under electrostatic conditions, the electric field inside a conductor

Does mirror reflect or absorb sound?

There is a small hole in a hollow sphere. The water enters into it when it is taken to a depth of $40\text{cm}$ under water. The surface tension of water is $0.07\text{N/m}$. The diameter of the hole is
[Take $g=10{\text{m/s}}^2$]

The uncertainty in the position of a moving bullet of mass $10gm$ is ${10}^{-5}m$. Calculate the uncertainty in its velocity

Consider a semicircle of radius $1$ unit constructed on the diameter $AB$, and let $O$ be its centre. Let $C$ be a point on $AO$ such that $AC:CO=2:1$. Draw $CD$ perpendicular to $AO$ with $D$ on the semicircle. Draw $OE$ perpendicular to $AD$ with $E$ on $AD$. Let $OE$ and $CD$ intersects at $H$. Then $DH$ equals

A system is shown in the figure. The time period for small oscillations of the two blocks will be:


(correct answer + 2, wrong answer - 0.50)

What should be the angle of projection for a body to have horizontal range equal to maximum height?

Four bodies of masses 1, 2, 3, 4 kg respectively are placed at the comers of a square of side 'a'. Coordinates of centre of mass are

The uncertainity in the position of an electron (mass $9.1\times {10}^{-28}g$) moving with velocity of $3.0\times {10}^{4}c{m}^{-1}$ accurate up to 0.011%, will be

I found the mention of 'oscillograph' in a numerical under the electrostatics chapter. Pls could you explain to me what this oscillograph actually is??

The degree of freedom of a gas is $6$. Gas can be

A steel wire having a radius of $2.0mm$, carrying a load of $4kg$, is hanging from a ceiling. Given that $g=3.1\pi m{s}^{-2}$, what will be the tensile stress that would be developed in the wire?

Which of the following is the reason for adsorption?

Find the temperature at which molecules of oxygen gas have the same rms speed as that of Helium atoms at $240\text{K}$.
$\{\text{Molecular mass of}{O}_2=32\text{g/mol}\&\text{He}=4\text{g/mol}\}$

The angular position of a particle about an axis is given by $\theta =6-8t+2t^2$. Then the angle between $\omega$ & $\alpha$ at t = 1 is

The tungsten filament of an electric lamp has a surface area A and a power rating P. If the emissivity of the filament is $ϵ$ and $\sigma$ is Stefan's constant, the steady temperature of the filament will be

A spherical body of radius $4\text{m}$ has a concentric cavity of radius $2\text{m}$ as shown in the figure. Thermal conductivity of the material is $\frac{100}{\pi }{\text{W/m}}^{\circ }\text{C}$. If the temperature of inner surface is kept at ${120}^{\circ }\text{C}$ and of the outer surface at ${40}^{\circ }\text{C}$. Then, find the temperature $T$ at a distance $3\text{m}$ from centre. (in ${}^{\circ }\text{C}$).

The latent heat of Vaporisation of a liquid at 500K and 1atm pressure is 30 Kcal/mole. What will be the change in internal energy of 3 mol of liquid at same temperature?

A linear harmonic oscillator of force constant $2\times {10}^6$ N/m times and amplitude 0.01 m has a total mechanical energy of 160 joules. Its

If $\overrightarrow{A}+\overrightarrow{B}$ is a unit vector along x - axis and $\overrightarrow{A}=\hat{i}-\hat{j}+\hat{k}$, then what is $\overrightarrow{B}$?

Electric field in the space is given as $\overrightarrow{E}=2x\hat{i}+y\hat{j}$, then charge enclosed inside cube of side length $2m$ as shown in figure will be

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane, another vector $\overrightarrow{C}$ lies outside this plane, then the resultant of these three vectors i.e., $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}$

If wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5\times {10}^{-5}mand{10}^{-4}m$ respectively, the ratio of their temperatures is

A uniform solid sphere of radius R, rolling without sliding on a horizontal surface with an angular velocity ${\omega }_0$, meets a rough inclined plane of inclination $\theta ={60}^{\circ }$.The sphere starts pure rolling up the plane with an angular velocity $\omega$ . Find the value of $\omega$.

Two forces $\overrightarrow{F_1}=(2\hat{i}+2\hat{j})N$ and $\overrightarrow{F_2}=(3\hat{j}+4\hat{k})N$ are acting on a particle. The component of force $\overrightarrow{F_1}$ along force $\overrightarrow{F_2}$ is

Calculate the mass of an $\alpha$ - particle. Its binding energy is 28.2 MeV.

Suppose a monochromatic X-ray, beam of wavelength 100 pm is sent through a Young's double slit and the interference pattern is observed on a photographic plate placed 40 cm away from the slit. What should be the separation between the slits so that the successive maxima on the screen are separated by a distance of 0.1 mm ?

A smooth sphere of mass 'M' moving with velocity 'u' directly collides elastically with another sphere of mass 'm' at rest. After collision their final velocities are 'V' and 'v' respectively. The value of 'v' is

A block of mass m is placed on a triangular block of mass M, which in turn is placed on a horizontal smooth surface as shown in figure. Assuming frictionless surfaces, find the velocity of the triangular block when the smaller block reaches the bottom end.

A body is moving from rest under constant acceleration and let $S_1$ be the displacement in the first $(p-1)$ seconds and $S_2$ be the displacement in the first $p$ seconds. The displacement in $(p^2-p+1{)}^{th}$ second will be

A tennis ball is dropped on a horizontal smooth surface. It bounces back after hitting the surface. The force on the ball during the collision is proportional to the degree of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to scale.

A glass marble whose mass is $200g$ falls from a height of $2.5m$ and rebounds to a height of $1.6m$. Find the change in momentum due to its rebound.

A body moves in a circle of radius $1\text{m}$. Its speed is given by $v=2t^2$. Find the net acceleration at $t=2\text{s}$