Which graph represents the difference between total energy and potential energy of a particle executing SHM vs it's distance from mean position ?

A bullet of $$10 \mathrm{~g}$$ leaves the barrel of gun with a velocity of $$600 \mathrm{~m} / \mathrm{s}$$. If the barrel of gun is $$50 \mathrm{~cm}$$ long and mass of gun is $$3 \mathrm{~kg}$$, then value of impulse supplied to the gun will be :

A planet having mass $$9 \mathrm{Me}$$ and radius $$4 \mathrm{R}_{\mathrm{e}}$$, where $$\mathrm{Me}$$ and $$\mathrm{Re}$$ are mass and radius of earth respectively, has escape velocity in $$\mathrm{km} / \mathrm{s}$$ given by:

(Given escape velocity on earth $$\mathrm{V}_{\mathrm{e}}=11.2 \times 10^{3} \mathrm{~m} / \mathrm{s}$$ )

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross - section. Cross sectional areas at $$\mathrm{A}$$ is $$1.5 \mathrm{~cm}^{2}$$, and $$\mathrm{B}$$ is $$25 \mathrm{~mm}^{2}$$, if the speed of liquid at $$\mathrm{B}$$ is $$60 \mathrm{~cm} / \mathrm{s}$$ then $$\left(\mathrm{P}_{\mathrm{A}}-\mathrm{P}_{\mathrm{B}}\right)$$ is :

(Given $$\mathrm{P}_{\mathrm{A}}$$ and $$\mathrm{P}_{\mathrm{B}}$$ are liquid pressures at $$\mathrm{A}$$ and $$\mathrm{B}$$% points.

density $$\rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$$

$$\mathrm{A}$$ and $$\mathrm{B}$$ are on the axis of tube

A vessel of depth '$$d$$' is half filled with oil of refractive index $$n_{1}$$ and the other half is filled with water of refractive index $$n_{2}$$. The apparent depth of this vessel when viewed from above will be-

The difference between threshold wavelengths for two metal surfaces $$\mathrm{A}$$ and $$\mathrm{B}$$ having work function $$\phi_{A}=9 ~\mathrm{eV}$$ and $$\phi_{B}=4 \cdot 5 ~\mathrm{eV}$$ in $$\mathrm{nm}$$ is:

$$\{$$ Given, hc $$=1242 ~\mathrm{eV} \mathrm{nm}\}$$

The rms speed of oxygen molecule in a vessel at particular temperature is $$\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v$$, where $$v$$ is the average speed of the molecule. The value of $$x$$ will be:

$$\left(\right.$$ Take $$\left.\pi=\frac{22}{7}\right)$$

The source of time varying magnetic field may be

(A) a permanent magnet

(B) an electric field changing linearly with time

(C) direct current

(D) a decelerating charge particle

(E) an antenna fed with a digital signal

Choose the correct answer from the options given below:

Two charges each of magnitude $$0.01 ~\mathrm{C}$$ and separated by a distance of $$0.4 \mathrm{~mm}$$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$$\vec{E}$$' of 10 dyne/C making $$30^{\circ}$$ angle with $$\vec{E}$$, the magnitude of torque acting on dipole is:

A disc is rolling without slipping on a surface. The radius of the disc is $$R$$. At $$t=0$$, the top most point on the disc is $$\mathrm{A}$$ as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

$$_{92}^{238}A \to _{90}^{234}B + _2^4D + Q$$

In the given nuclear reaction, the approximate amount of energy released will be:

[Given, mass of $${ }_{92}^{238} \mathrm{~A}=238.05079 \times 931.5 ~\mathrm{MeV} / \mathrm{c}^{2},$$

mass of $${ }_{90}^{234} B=234 \cdot 04363 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2},$$

mass of $$\left.{ }_{2}^{4} D=4 \cdot 00260 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2}\right]$$

Under isothermal condition, the pressure of a gas is given by $$\mathrm{P}=a \mathrm{~V}^{-3}$$, where $$a$$ is a constant and $$\mathrm{V}$$ is the volume of the gas. The bulk modulus at constant temperature is equal to

Two trains 'A' and 'B' of length '$$l$$' and '$$4 l$$' are travelling into a tunnel of length '$$\mathrm{L}$$' in parallel tracks from opposite directions with velocities $$108 \mathrm{~km} / \mathrm{h}$$ and $$72 \mathrm{~km} / \mathrm{h}$$, respectively. If train 'A' takes $$35 \mathrm{~s}$$ less time than train 'B' to cross the tunnel then. length '$$L$$' of tunnel is :

(Given $$\mathrm{L}=60 l$$ )

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions :

Different combination of 3 resistors of equal resistance $$\mathrm{R}$$ are shown in the figures. The increasing order for power dissipation is:

For the following circuit and given inputs A and B, choose the correct option for output '$$Y$$'

A body of mass $$(5 \pm 0.5) ~\mathrm{kg}$$ is moving with a velocity of $$(20 \pm 0.4) ~\mathrm{m} / \mathrm{s}$$. Its kinetic energy will be

The ratio of powers of two motors is $$\frac{3 \sqrt{x}}{\sqrt{x}+1}$$, that are capable of raising $$300 \mathrm{~kg}$$ water in 5 minutes and $$50 \mathrm{~kg}$$ water in 2 minutes respectively from a well of $$100 \mathrm{~m}$$ deep. The value of $$x$$ will be

Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :

When a resistance of $$5 ~\Omega$$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $$250 \mathrm{~mA}$$, however when $$1050 ~\Omega$$ resistance is connected with it in series, it gives full scale deflection for 25 volt. The resistance of galvanometer is ____________ $$\Omega$$.

A fish rising vertically upward with a uniform velocity of $$8 \mathrm{~ms}^{-1}$$, observes that a bird is diving vertically downward towards the fish with the velocity of $$12 \mathrm{~ms}^{-1}$$. If the refractive index of water is $$\frac{4}{3}$$, then the actual velocity of the diving bird to pick the fish, will be __________ $$\mathrm{ms}^{-1}$$.

The radius of $$2^{\text {nd }}$$ orbit of $$\mathrm{He}^{+}$$ of Bohr's model is $$r_{1}$$ and that of fourth orbit of $$\mathrm{Be}^{3+}$$ is represented as $$r_{2}$$. Now the ratio $$\frac{r_{2}}{r_{1}}$$ is $$x: 1$$. The value of $$x$$ is ___________.

A potential $$\mathrm{V}_{0}$$ is applied across a uniform wire of resistance $$R$$. The power dissipation is $$P_{1}$$. The wire is then cut into two equal halves and a potential of $$V_{0}$$ is applied across the length of each half. The total power dissipation across two wires is $$P_{2}$$. The ratio $$P_{2}: \mathrm{P}_{1}$$ is $$\sqrt{x}: 1$$. The value of $$x$$ is ___________.

In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. $$\frac{E^{a}}{2 b} \mathrm{~J} / s$$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $$\frac{b}{a}$$ will be __________.

At a given point of time the value of displacement of a simple harmonic oscillator is given as $$\mathrm{y}=\mathrm{A} \cos \left(30^{\circ}\right)$$. If amplitude is $$40 \mathrm{~cm}$$ and kinetic energy at that time is $$200 \mathrm{~J}$$, the value of force constant is $$1.0 \times 10^{x} ~\mathrm{Nm}^{-1}$$. The value of $$x$$ is ____________.

A thin infinite sheet charge and an infinite line charge of respective charge densities $$+\sigma$$ and $$+\lambda$$ are placed parallel at $$5 \mathrm{~m}$$ distance from each other. Points 'P' and 'Q' are at $$\frac{3}{\pi}$$ m and $$\frac{4}{\pi}$$ m perpendicular distances from line charge towards sheet charge, respectively. '$$\mathrm{E}_{\mathrm{P}}$$' and '$$\mathrm{E}_{\mathrm{Q}}$$' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $$\frac{E_{p}}{E_{0}}=\frac{4}{a}$$ for $$2|\sigma|=|\lambda|$$, then the value of $$a$$ is ___________.

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $$\pi: 22$$ then, the value of its angular speed will be ____________ $$\mathrm{rad} / \mathrm{s}$$.

The elastic potential energy stored in a steel wire of length $$20 \mathrm{~m}$$ stretched through $$2 \mathrm{~cm}$$ is $$80 \mathrm{~J}$$. The cross sectional area of the wire is __________ $$\mathrm{mm}^{2}$$.

$$\left(\right.$$ Given, $$\left.y=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$$