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The average translational kinetic energy of molecules of an ideal gas is (symbols have their usual meanings)

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut - off, the coordinates of the centre of mass of the remaining portion will be

What is the effective capacitance between points $X$ and $Y?$

The Bat Life: What can be said with 100% confidence about the temperatures at point $P_{1}and{P}_2$?

Among two interfering sources, let sound waves from source $S_1$, be ahead of the phase by ${90}^{\circ }$ relative to that of $S_2$. At an observation point $P$, if $P{S}_1-P{S}_2=1.5\lambda$, then the phase difference between the waves from $S_1$ and $S_2$ reaching $P$ is

The linear charge density of a uniform semicircular wire varies with $\theta$ as shown in the figure as $\lambda ={\lambda }_0\cos \theta$. Find the charge on the wire if $R$ is the radius of the ring.

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is

If force $\left(F\right)$, velocity $\left(V\right)$ and time $\left(T\right)$ are taken as fundamental units, then dimensions of mass are

A thin rod of mass M and length l stands along z-axis. Its lower end is hinged at the center of a disc of same mass M and radius R. The disc is on XY plane with its center at the origin. The whole arrangement is rotating freely about z-axis with an angular velocity ${\omega }_0$ .If the rod falls on disc and rotates with the disc. The angular speed of the arrangement is

The capacitance of a parallel plate capacitor with air as medium is $6\mu \text{F}$. With the introduction of a dielectric medium, the capacitance becomes $30\mu \text{F}$. The permittivity of the medium is: ${\epsilon }_0=8.85\times {10}^{-12}{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$

The amount of heat generated in a coil of resistance $R$ due to a charge $q$ passing through it if the current in the coil, decreases down to $0$ uniformly during a time internal $t_o$ is -

A uniform magnetic field B exists in the region between $x=0$ and $x=\frac{3R}{2}$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum $p$ directed along x-axis enters region 2 from region 1 at point $P_1(y=-R)$. Which of the following option(s) is/are correct?

Two particles each of mass m are connected by a string of length 1m. The particles are kept on a smooth horizontal plane. The initial separation between the particles is 0.5 m. One of the particles is given a velocity 18 m/s as shown. Find the magnitude of angular velocity of one particle with respect to the other particle just after the string becomes taut (in rad/s). ___

A bead $A$ can slide freely along a smooth rod bent in the form of a half circle of radius $R$. The system is set in rotation with a constant angular velocity $\omega$ about a vertical axis OO'. Find the angle $\theta$ corresponding to steady position of the bead.

In an npn transistor, the collector current is 24 mA. If 80% of electrons reach collector, its base current in mA is

The magnitude of saturation photoelectric current depends upon

A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed to 4 m/s relative to the trolley in a direction opposite to the trolley's motion and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

Explain total internal reflection, with the help of a neat diagram.

An object is placed at a distance of 40 cm from a thin converging lens of focal length 10 cm. The image distance is .

If $\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{B}\times \overrightarrow{A}$, then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is

In an intrinsic semiconductor, the number of conduction electrons is $9\times {10}^{19}$ per cubic meter. Find the total number of current carriers $\left(\text{electrons and hole}\right)$ in a semiconductor of size $1\text{cm}\times 1\text{cm}\times 1\text{mm}$

What substance can layers of decayed plants under the earth's crust form over time?

A resistance $R$, an inductance $L$ and a capacitor $C$ are all connected in series with an $AC$ supply. The resistance is of $16\Omega$ and for a given frequency, the inductive reactance of $L$ is $24\Omega$ and capacitance reactance of $C$ is $12\Omega$. If the current in the circuit is $5\text{A}$, find the potential difference across $R,L\text{and}C$ in $\left(\text{V}\right)$.

A vessel of depth $2h$ is half filled with a liquid of refractive index $2\sqrt{2}$ ​ and the upper half with another liquid of refractive index $\sqrt{2}$. The liquids are immiscible. The apparent depth of an object which has a height $\frac{h}{2}$ from the bottom of the vessel inside the liquid as seen from the top of the vessel is

Find the acceleration of C w.r.t. ground. Given that acceleration of A is $a$ to the right and acceleration of B is $b$ to the left

Radiation of wavelength $\lambda$ is incident on a photocell. The fastest emitted electron has a speed $v$. If the wavelength is changed to $\frac{3\lambda }{4}$, the speed of the fastest emitted electron will be :

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes 2 cm, $1m{s}^{-1}$ and $10m{s}^{-2}$ at a certain instant. Find the amplitude and the time period of the motion.

At a certain place, the horizontal as well as vertical components of earth's magnetic field is $B_0$. The total magnetic field intensity at the place will be,

A solid conducting sphere having a charge $Q$ is surrounded by an uncharged concentric conducting spherical shell. Let the potential difference between the surface of the solid sphere and the outer surface of the shell be $V.$ If the shell is now given a charge $-3Q,$ the new potential difference between the same two surfaces is:

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