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A box contains $N$ molecules of a perfect ideal gas at temperature $T_1$ and pressure $P_1$. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is $P_2$ and new temperature is $T_2$, then

The acceleration of $A$ is as shown in the figure. If the system starts from rest, find the velocity with which the wedge hits the wall. $A$ is constrained to move only in vertical direction.

Three uniform bricks each of length $60\text{cm}$ and mass $m$ are arranged as shown in the figure. Considering only the length of the bricks, find the distance of centre of mass of the system of bricks from the wall.

The unit vector along $\overrightarrow{A}\times \overrightarrow{B}$ is

If the velocity head of a stream of water is equal to $10\text{cm}$, then its speed of flow is approximately

If ring and sphere both of same mass are rotated then which of them will come to rest first ? And which is easy to rotate? And the relation of moment of inertia with rotation?

A block of mass m rigidly attached with a spring k is compressed through a distance A. If the block is released, the period of oscillation of the block for a complete cycle is equal to

A container has two layers of immiscible liquids $1$ and $2$ with refractive indices $1.5$ and $4/3$ respectively. What is apparent position of an object placed at the bottom of the vessel. Thickness of the layers are $3\text{cm}$ and $8\text{cm}$ respectively?

A simple pendulum has a time period $T_1$ when on earth's surface and $T_2$ when taken to a height R above the earth's surface, where R is the radius of the earth. The value of $\frac{T_2}{T_1}$ is

In the above problem, if the lift moves up with a constant velocity of 2 m/sec, the reading on the balance will be

Mass M is divided into two parts xM and (1 − x)M. For a given separation, the value of x for which the gravitational attraction between the two pieces becomes maximum is

Two particles of equal mass go round a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

A stationary body explodes into three identical fragments such that two of them fly off mutually perpendicular to each other, each with same kinetic energy, $E_o$. The energy of the explosion is

A particle starting from rest moves with constant acceleration. If it takes 5.0 s to reach the speed 18km/h find.

(a) The average velocity during this period and

(b) The distance travelled by the particle during this period.

For the first order reaction A give rise to 2B+C the initial pressure is P_{​​​​​​A}=90mmhg h the pressure after 10 min is 180mmhg find k ???

6*10 ^-2 sec -1

Put it on paper

A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is $200m{s}^{-1}$ and the amplitude is 0.5 cm. Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x = 50 cm has reached its maximum displacement.

A dipole $P_1$ is placed as shown in figure. Then work done to bring another dipole $P_2$ from infinity to separation r from $P_1$ as shown in figure is.

Time taken by the projectile to reach from $A$ to $B$ is $t$. Then, the distance $AB$ is equal to

In the L – R circuit shown in the figure, the key K is closed at time t = 0.

A nucleus with Z = 92 emits the following in a sequence :
$\alpha ,\beta -,\beta -,\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,\beta -,\beta -,\beta +,\alpha ,\beta +,\alpha$
The Z of the resulting nucleus is

A sound consists of four frequencies : $200\text{Hz},400\text{Hz},1125\text{Hz}$ and $1600\text{Hz}$. A sound filter is made by passing this sound through a bifurcated pipe as shown. The sound wave has to travel a distance $40\text{cm}$ more in the right branch than in the straight pipe. The speed of sound in air is $300\text{m/s}$. which of the given frequencies will almost completely muffle or silence the outlet?

The velocity of water waves may depend on their wavelength $\lambda ,$ the density of water p and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as

The radii of the inner and outer spheres of a condenser are 9 cm and 10 cm respectively. If the dielectric constant of the medium between the two spheres is 6 and charge on the inner sphere is $18\times {10}^{-9}$ coulomb, then the potential of inner sphere will be, if the outer sphere is earthed

A 20 cm long capillary tube is dipped in water. The water rises upto 8 cm. if the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

Current ‘I' flows through along wire. A square loop made of conducting wire held below the wire in

The same vertical plane is released and allowed to fall under gravity.If acceleration of the loopis‘a’ then

A tuning fork is placed near a vibrating stretched wire. If frequency of tuning fork is greater than frequency of stretched wire, then a boy standing near the two hears a beat frequency f.

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{(A) If tuning fork is loaded with wax}& \text{(p) Beat frequency must increase}\\ \text{(B) If prongs of tuning fork are filed}& \text{(q) Beat frequency must decrease}\\ \text{(C) If tension in stretched wire is increased}& \text{(r) Beat frequency may increase}\\ \text{(D) If tension in stretched wire is decreased}& \text{(s) Beat frequency may decrease}\end{array}$

A uniform rod of length $L$ is free to rotate in a vertical plane about a fixed horizontal axis through $B$. The rod begins rotating from rest from its unstable equilibrium position. When it has turned through an angle $\theta$, its angular velocity $\omega$ is given as:

Convert $\frac{\pi }{4}$ radians to degrees

An elevator accelerates upwards at a constant rate. A uniform string of length $L$ and mass $m$ supports a small block of mass $M$ that hangs from the ceiling of the elevator. The tension at distance $l$ from the ceiling is $T$. The acceleration of the elevator is

Light of wavelength 6000 Armstrong in air enters a medium of refractive index of 1.5 . What are the wavelength and frequency of light in that medium?

Can you please tell me that why I should take

v=3*10(raised to 8)/6000 Armstrong

Instead I can take v=3*10(raised to 8)/4000 Armstrong , because wavelength of light in that medium is 4000 Armstrong.

The phase difference between the displacement wave and the pressure wave in sound wave is

Radius of gyration of a uniform disc about a line perpendicular to the plane of disc is equal to its radius $R$. If the distance of the line from the center is $\frac{R}{\sqrt{x}},$ find the value of $x$.

In dot product,

i.i=1x1xcos theta(How does cos comes here?)

A particle is placed at the origin and a force $F=kx$ is acting on it (where, $k$ is a positive constant). If $U\left(0\right)=0$, the graph of $U\left(x\right)$ versus $x$ will be (where $U$ is the potential energy function)

$E_{0}and{E}_h$ respectively represent the average kinetic energy of a molecule of oxygen and hydrogen. If the two gases are at the same temperature, which of the following statements is true?

Why a transverse wave can be either mechanical or non-mechanical wave ?

A food packet is dropped from a plane going at an altitude of 100 m. What is the path of the packet as seen from the plane?

Each capacitor shown in figure (31-E10) has a capacitance of $5.0\mu F.$ The emf of the battery is 50 V. How much charge will flow through AB if the switch S is closed ?