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A cube is compressed at $0^{\circ }C$ equally from all sides by an external pressure p. By what amount should the temperature be raised to bring it back to the size it had before the external pressure was applied? (Given K is bulk modulus of elasticity of the material of the cube and $\alpha$ is the coefficient of linear expansion)

A wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to this current, the temperature of the wire is raised by $\Delta T$ in a time $t$. A number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature of wire is raised by same amount $\Delta T$ in the same time $t$. Find the value of $N$.

An inductor of inductance $L,$ a capacitor of capacitance $C$ and a resistor of resistance $R$ are connected in series to an ac source of potential difference $V\text{volt}$ as shown in figure. Potential difference across $L,C$ and $R$ is $40\text{V},10\text{V}$ and $40\text{V},$ respectively. The amplitude of current flowing through $LCR$ series circuit is $10\sqrt{2}\text{A}.$ The impedance of the circuit is

In the arrangement shown in the fig the cylinder is insulating one. Both sides same diatomic gas is trapped by two insulting massless pistons with the help of an ideal spring. The natural length of the spring is equal to the length of the cylinder. Initial state of the gases are as shown in the figure.

What is the value of energy stored in the spring?

A projectile is fired at ${30}^{\circ }$ to the horizontal. The vertical component of its velocity is $80m{s}^{-1}$. Its time of flight is T. What will be the velocity of the projectile at $t=\frac{T}{2}$

A string of length L fixed at both ends vibrates in its fundamental mode at a frequency v and a maximum apmplitude A. (a) Find the wavelength and the wave number k. (b) Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along the direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.

The density $\rho$ of a liquid varies with depth $h$ from the free surface as $\rho =kh$. A small body of density ${\rho }_1$ is released from the surface of the liquid. The body executes $SHM$ with amplitude

The radius of gyration of uniform rod of length L and mass M about an axis passing through its centre and perpendicular to its length is

A point moves in x-y plane according to the law x=4 sin 6t and y=4(1-cos 6t). The distance traversed by the particle in 4 seconds is (x and y are in meters)

A particle traversed half of the distance with a velocity $v_0$. The remaining part of the distance was covered with velocity $v_1$ for half the time and with velocity $v_2$ for the other half of the time. The mean velocity of the particle averaged over the whole time of motion is

A ball is allowed to fall from a height of 10m. If there is 40% loss of energy due to impact then after one impact ball will go up by??

1. 80

Consider a situation similar to that of the previous problem except that the ends of the rod slide on a pair of thick metallic rails laid parallel to the wire. At one end the rails are connected by resistor of resistance R. (a) What force is needed to keep the rod sliding at a constant speed v ? (b) In this situation what is the current in the resistance R? (c) Find the rate of heat developed in the resistor. (d) Find the power delivered by the external agent exerting the force on the rod.

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 average angular velocity $\omega$ is given as:

An object is projected with a velocity of $20\text{m/s}$ making an angle of ${45}^{\circ }$ with horizontal. The equation for the trajectory is $h=Ax-B{x}^2$ where $h$ is height, $x$ is horizontal distance, A and B are constants. The ratio A : B has value of $(g=10m{s}^{-2})$

Find the current in the circuit consisting of batteries with internal resistance as shown.

An inductor of inductance $5.0\text{H}$ having a negligible resistance is connected in series with a $100\Omega$ resistor and a battery of emf $2\text{V}$. Find the potential difference across the resistor $20\text{ms}$ after the circuit is switched on.



$[$Use $(1-e^{-0.4})=0.33]$

A particle is moving in the $x-y$ plane with uniform speed $v$. The equation of trajectory for the particle is represented by the parabola $y=a{x}^2,$ where $a$ is a $+ve$ constant. Find the radius of curvature of trajectory at the point $x=0$.

Two polaroids are present in the path of unpolarized beam of intensity $I_0$ such that no light is emitted from the second polaroid. If a third polaroid, whose transmission axis makes an angle $\theta$ with the transmission axis of the first polaroid, is placed between these polaroids. Then the intensity of light emerging from the last polaroid will be,

An inductor-coil carries a steady-state current of 2.0 A when connected across an ideal battery of emf 4.0 V. If its inductance is 1.0 H, find the time constant of the circuit.

A spherical conductor of radius $50\text{cm}$ has charge of $3.6\mu \text{C}$ distributed over its surface. What is magnitude of electric field at a point $150\text{cm}$ from the centre of the conductor?

Tangential acceleration of a particle moving in a circle of radius $1\text{m}$ varies with time $t$ as shown in the figure (initial velocity of particle is zero). Time after which total acceleration of particle makes an angle of ${30}^{\circ }$ with radial acceleration is

For the following circuit, identify the equivalent gate.

A $200\text{Hz}$ sinusoidal wave is travelling in the positive $x$-direction along a string with a linear mass density of $4\times {10}^{-3}\text{kg/m}$ and a tension of $40\text{N}$. At time $t=0$, the point $x=0$ has maximum displacement in the positive $y$-direction. Next when this point has zero displacement, the slope of the string is $\frac{\pi }{20}$. Which of the following expressions respresent the displacement of string as a function of $x$ (in metre) and $t$ (in seconds).

What is the reading of the following screw gauge?

In the diagram shown below, all three rods are of equal length $L=1\text{m}$ and equal mass $M=3\text{kg}$. The system is rotated such that rod $B$ is the axis. What is the moment of inertia of the system?

The potential energy of a certain particle is given by $U=\frac{1}{2}(x^2-z^2)$. The force on it is: