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A certain amount of an ideal gas is initially at a pressure $P_1$ and temperature $T_1$. First, it undergoes an isobaric process 1 - 2 such that $T_2=\frac{3T_1}{4}$. Then, it undergoes an isochoric process $2\to 3$ such that $T_3=\frac{T_2}{2}$. The ratio of the final volume to the initial volume of the ideal gas is

10^-3 W of 5000 $\text{Å}$ Light is directed on a photoelectric cell. If the current in the cell is 0.16 μA, the percentage of incident photons which produce photoelectrons, is

A stone thrown from a point on the ground at ${30}^{\circ }$ to the horizontal to hit another point on the ground $145\text{m}$ away, fell short by $5\text{m}$. A second trial at a different angle (but the same speed) again fell short by the same distance. What was the difference in their flight times ?

Consider two uniform discs of the same thickness and different radii $R_1=R\text{and}{R}_2=\alpha R$, made of the same material. If the ratio of their moments of inertia $I_1$ and $I_2$, respectively, about their axes is $I_1:I_2=1:16$, then the value of $\alpha$ is :

Let f(x) = sin x + cos x, $g\left(x\right)=x^2-1$. Thus g(f(x)) is invertible for x$\in$

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should be

A circuit contains two inductors of self-inductance $L_1$ and $L_2$ in series. If $M$ is the mutual inductance, then the effective inductance of the circuit shown will be

In a simple gear train in shown in figure below, the absolute speeds of different wheels, when wheel 4 is the driver.

A body is attached to the lower end of a vertical spiral spring and it is gradually lowered to its equilibrium position. This stretches the spring by a length $d$. If the same body attached to the same spring is allowed to fall suddenly, what would be the maximum stretching in this case?

The value of $\underset{-1}{\overset{0}{\int }}\frac{dx}{x^2+2x+2}$ is:

A circular disc with a groove along its diameter is placed horizontally. A block of mass $1\text{kg}$ is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $\mu =\frac{2}{5}$. The disc has an acceleration of $25\text{m}/s^2$ Find the acceleration of the block with respect to disc.

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

A square plate of mass 120 g and edge 5.0 cm rotates about one of the edges. If it has a uniform angular acceleration of $0.2rad/s^2$, what torque acts on the plate ?

Determine the recoil speed of a deuterium atom when a photon of energy $10.2\text{eV}$ is emitted in a forward direction.

Show that the altitude of the right circular cone of maximum volume that can be iscribed in a sphere of radius r is $\frac{4r}{3}.$

A cart is moving horizontally along a staight line with a constant speed $30\text{m/s}$. A bullet is to be fired vertically upwards from the moving cart in such a way that it returns to the cart at the same point from where it was fired, after the cart has moved $80\text{m}$. At what speed (relative to the cart), the bullet must be fired ? Take $g=10{\text{m/s}}^2$.

In a rectangle ABCD, BC = 2 AB. The moment of inertia is minimum along axis through

(a) Find the radius of the circular orbit of a satellite moving with an angular speed equal to the angular speed of earth's rotation (b) if the satellite is directly above the north pole at some instant, find the time it takes to come over the equatorial plane. Mass of the earth $=6\times {10}^{24}$kg.

A composite rod of mass '2m' $\&$ length '2l' consists of two identical rods joined end to end at P. The composite rod is hinged at one of its ends and is kept horizontal. If it is released from rest, ·Find its angular speed when it becomes vertical

PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity V as shown. The force needed to maintain constant speed of EF is (No gravity is there)

Find the apparent depth of the object, as seen by the observer.

[measured from the surface $\text{AB}$]

1. 547.82

A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure. ${\mu }_s$ is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is:

What is the average molecular mass in dry air (78% N₂ and 22%O₂​​​​​​)

If the temperature of a gas is increased from ${27}^{\circ }$ C to ${927}^{\circ }$C, the root mean square speed of its molecules

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ to and then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done is W. Then

In the figure shown, natural length of the spring $=2\text{m}$. Force constant $k=200\text{N/m}$. find the reading of the spring balance if $A$ is kept at rest and $B$ is displaced of the right by $1\text{m}$. Take $g=10m/s^2$