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An alternating voltage E =50 sin(100 t)V is connected to a 1 μF capacitor through an ac ammeter. What will be the reading of the ammeter?

In the measurement of the acceleration due to gravity using a simple pendulum, the percentage error in the measured value of the length of the pendulum is $2\%$ and that in the time period of oscillation is $1\%$. The percentage error in the measured value of the acceleration due to gravity is

An electric field is expressed as $\overrightarrow{E}=2\hat{i}+3\hat{j}$. Find the potential difference $(V_A-V_B)$ between two points A and B whose position vectors are given by $r_A=\hat{i}+2\hat{j}$ and $r_B=2\hat{i}+\hat{j}+3\hat{k}.$

Two equal masses are connected by a spring satisfying Hooke's law and are placed on a frictionless table. The spring is elongated a little and allowed to oscillate. Let the angular frequency of oscillations be $\omega$. Now one of the masses is stopped. The square of the new angular frequency is $\frac{{\omega }^2}{x}$, where $x$ is

Consider the electronic energy level diagram of H-atom. Photons associated with shortest and longest wavelengths would be emitted from the atom by the transitions labeled

If the radius of first Bohr orbit is x, then de-Broglie wavelength of electron in $3^{rd}$ orbit is nearly:

In the circuit, as shown in the figure, if the value of R.M.S current is 2.2 A, the power factor of the box is

Two identical parallel plate capacitors are connected in series and then joined in series with a battery of 100 V. A slab of dielectric constant K = 3 is inserted between the plates of the first capacitor. Then, the potential difference across the capacitors will be, respectively,

A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is $(\angle POQ={40}^{\circ })$

The graph shows the variation of $\frac{1}{v}$ (where $v$ is the velocity of the particle) with respect to time. Then find the value of acceleration at $t=3\text{sec}$

Two charges of magnitude -4C and 4C are placed at points (1, 2, 3) and (3, 4, 2) respectively. What is the dipole moment?

In the circuit shown below, all three voltmeters are identical and ideal. Each resistor has the same given resistance R. Voltage V is also given to be 9V. Find the reading of voltmeter $V_3$ (in volts).

Potential energy curve a of a body of mass $m=2kg$ is shown in the figure, it is released from rest at point A. Maximum distance covered by it on the positive $x-$axis from the origin till it momentarily comes to rest is

A block of mass $1\text{kg}$ is kept on an inclined accelerating conveyor belt. Acceleration of the belt is $1{\text{m/s}}^2$ as shown in figure. Minimum coefficient of static friction between the belt and block to prevent slipping of the block will be: [Take $g=10{\text{m/s}}^2$]

A source of sound S and a detector D are placed at some distance from one another. A big cardboard is placed near the detector and perpendicular to the line SD as shown in figure. It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is $336\frac{m}{s}$?

A body is moved along a straight line path by a machine delivering constant power. The distance moved by the body in time t is proportional to:

An object kept at $\text{O}$ is in equilibrium under the action of four coplanar forces shown in the figure. Find the magnitudes of $F_1$ and $F_2$.

According to photon theory of light which of the following physical quantities associated with a photon do not/does not change as it collides with an electron in vacuum

For photoelectric emission from a certain metal the cut off frequency is v. If radiation of frequency 2v impinges on the metal plate, the maximum possible velocity of the emitted electron will be (m is the electron mass).

At t = 0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a wire is described by the function $y=\frac{6}{x^2}giventhatx\ne 0$. Transverse velocity of a particle at x = 2 m and t = 2 s is

The initial pressure and volume of a given mass of a gas $(\frac{C_p}{C_v}=\gamma )$ are $P_0$ and $V_0$ The gas can exchnage heat with the surrounding,

(a) It is slowely comproessed to a volume $\frac{V_0}{2}$ and then suddenly compressed to $\frac{V_0}{4}$. Find the final presure.

(b) If the gas is suddenly compressed from the volume $V_0$ to $\frac{V_0}{2}$ and then slowly compressed to $\frac{V_0}{4}$, what will be the final pressure ?

A smooth sphere of radius R is made to translate in a straight line with a constant acceleration a. A particle kept on the top of the sphere is released from there at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as function of the angle $\theta$ it slides.

A series combination of $0.1M\Omega$ resistor and a $10\mu F$ capacitor is connected across a 1.5 V source of negligible resistance. The time (in seconds) required for the capacitor to get charge up to 0.75 V is approximately

In the figure shown, stiffness of spring is k and mass of the block is m. The pulley is fixed. Initially the spring is relaxed. Now the system is released from rest. The maximum elongation in the spring is

Two blocks, $4\text{kg}$ and $2\text{kg}$ are sliding down an incline plane as shown in figure. The acceleration of $2\text{kg}$ block is (Take $g=10{m/s}^2$)

The figure shows the various positions [labelled subscripts] of small magnetised needles P and Q. The arrows show the direction of their magnetic moment. Which configuration corresponds to the lowest potential energy of all the configurations shown?

Three identical vessels A, B and C contain same quantity of liquid. In each vessel balls of different densities but same masses are placed. In vessel A, the ball is partly submerged; in vessel B, the ball is completely submerged but floating and in vessel C, the ball has sunk to the base. If $F_A$, $F_B$ and $F_C$ are the total forces acting on the base of vessels A, B and C respectively, then

A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are $60\text{V}$ and $40\text{V}$ respectively.
At what frequency, the current in the circuit lags the voltage by ${45}^{\circ }$?

Fractional change in the radius of a sphere of bulks modulus $B$, when it is compressed by pressure $P$ from all sides is

The operating temperature of a tungsten filament in an incandescent lamp is $2000\text{K}$ and its emissivity is $0.3$. Find the surface area of the filament of a $25\text{watt}$ lamp.
Stefen's constant $\sigma =5.67\times {10}^{-8}{\text{W m}}^{-2}{\text{K}}^{-4}$

If the earth stops rotating, the apparent value of g on its surface will

A line passes from $(3,4)$ having $y$-intercept $c=2$. Find the slope of the line.

For the series L-C-R circuit shown in the figure, the resonance frequency and the current at the resulting resonating frequency will be

Figure shows a block $A$ of mass $6m$ having a smooth semicircular groove of radius $a$ placed on a smooth horizontal surface. A block $B$ of mass $m$ is released from rest from horizontal position as shown in the figure. Find the speed of the bigger block $6m$, when the smaller block reaches the bottommost position of the groove. Take $g=10{\text{m/s}}^2$.

An ideal monoatomic gas is confined in a cylinder by a spring-loaded piston of cross-sectional area $8\times {10}^{-3}{\text{m}}^2$. Initially the gas is at $300\text{K}$ and occupies a volume of $2.4\times {10}^{-3}{\text{m}}^3$. The spring is in a relaxed state. The gas is heated by a small heater coil $H$. The force constant of the spring is $8000\text{N/m}$ and the atmospheric pressure is $1.0\times {10}^5\text{Pa}$. The cylinder and piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and cylinder. There is no heat loss through the heater coil wire and thermal capacity of the heater coil is negligible. With all the above assumptions, if the gas is heated by the heater until the piston moves out slowly by $0.1\text{m}$, then the final temperature is -

A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2\text{sec}$ it rotates through an angle ${\theta }_1$, in the next $2\text{sec}$ it rotates through an additional angle ${\theta }_2$. The ratio of $\frac{{\theta }_2}{{\theta }_1}$ is

A chain of length $L=10\text{m}$ and mass $m=20\text{kg}$ is allowed to fall on a table such that the part falling on the table comes to rest immediately. The force acting on the table when $5\text{m}$ of it has fallen on the table is [Take $g=10{\text{m/s}}^2$]

Compare the radius of curvature at different points on the curve shown in the figure.

Which of the following does not affect the motion of a moving electron?

A particle moves along parabolic path $x=y^2+2y+2$ in such a way that $y-$ component of velocity is constant and equal to $5\text{m/s}$ during the motion. Magnitude of acceleration of the particle

A particle projected from ground moves at an angle ${45}^{\circ }$ with horizontal one second after projection and speed is minimum two seconds after the projection. The angle of projection of particle is
[Neglect the effect of air resistance]

A particle located at $x=0$ at time $t=0$, starts moving along the positive $x-$direction with a velocity $v$ that varies as $v=\alpha \sqrt{x}.$ The displacement of the particle varies with time as

A ray falls on a prism ABC (AB = BC) and travel as shown in figure. The least value of refractive index of material of the prism should be

A Force $\overrightarrow{F}=(6\hat{i}+4\hat{j}-2\hat{k})\text{N}$ is applied on a block which is moving with velocity $\overrightarrow{v}=(8\hat{i}+12\hat{j}-3\hat{k})\text{m/s}$. The instantaneous power applied to the particle is

Explain the formation of colours in thin films (example soap film).

The length and breadth of a rectangle are $(5.7\pm 0.1)cm$ and $(3.4\pm 0.2)cm$. Calculate area of the rectangle with error limits.