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A series $\text{AC}$ circuit containing an inductor $\left(20\text{mH}\right)$, a capacitor $\left(120\mu \text{F}\right)$ and a resistor $60\Omega$ is driven by an $\text{AC}$ source of $24\text{V},50\text{Hz}$. The energy dissipated in the circuit in $60\text{s}$ is

Three concentric metallic spherical shells of radii R, 2R, 3R are given charges Q1, Q2, Q3 respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells Q1 : Q2 : Q3 is

Infrared radiation is detected by

If lighter object in the earth attract earth with the Same force as earth attract it,why does it fall?

Why gravitational force is so called action reaction pair?

The average thermal energy for a mono-atomic gas is :

($k_B$ is Boltzmann constant and $T$ is absolute temperature)

A series $LCR$ circuit is connected to an ac voltage source. When $L$ is removed from circuit, the phase difference between current and voltage is $\frac{\pi }{4}$. If instead of $L,C$ is removed from the circuit, the phase difference between current and voltage is again $\frac{\pi }{4}$. The power factor of the original circuit is

A vessel contains oil (density = $0.8{\text{g/cm}}^3)$ over mercury (density = $13.6{\text{g/cm}}^3)$. A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in ${\text{g/cm}}^3$ is

A galss prism of refractive index $1.5$ is immersed in water (refractive index $\frac{4}{3}$). A light beam incident normally on the face AB is totally reflected to reach the face BC, if

In the figure, a parallel beam of light is incident on the plane of the slits of Young's double-slit experiment. Light incident on the slit $S_1$ passes through a medium of variable refractive index $\mu =1+ax$ (where $x$ is the distance from the plane of slits as shown), up to a distance $l$ before falling on $S_1$. The rest of the space is filled with air. If at $O$ minima is formed, then the minimum value of the positive constant $a$ ( in terms of $l$ and wavelength $\lambda$ in air) is

A rigid rod of mass $m$, with a ball of mass $M$ attached to the free end is restrained to oscillate in a vertical plane as shown in the figure. Find the natural frequency of oscillation.

The length of cylinder is measured with a metre rod having least count $0.1\text{cm}$. Its diameter is measured with vernier caliper having least count $0.01\text{cm}$. Given that length is $5.0\text{cm}$ and diameter is $4.0\text{cm}$. The percentage error in the calculated value of the volume will be

An unpolarised light is incident upon a glass plate of refractive index 1.54 at Brewster’s angle and gets completely plane polarized. The angle of polarization is: $(giventan{57}^{\circ }=1.54$)

Two small identical conducting balls $A$ and $B$ of charges $+10\mu \text{C}$ and $+30\mu \text{C}$ respectively are kept at a separation of $50\text{cm}$. These balls have been connected by a wire for a short time.



$\left(\text{ii}\right)$ The electrostatic force between the balls will be



​​​​​​​$[$1 Mark$]$

Vibration in a string of length $60\text{cm}$ fixed at both ends is represented by the equation, $y=4\sin \left(\frac{\pi x}{15}\right)\cos \left(96\pi t\right)$, where $x$ and $y$ are in $\text{cm}$ and $t$ in $\text{s}$. The number of loops formed in vibrating string will be

When the load on a wire is slowly increased from 3 to 5 $kg-wt$, the elongation increases from $0.61mm$ to $1.02mm$. The work done during the extension of wire is

Amplitude of electric field in a laser beam of power 4.4 mW with cross-sectional area of $2m{m}^2$ is

The electric potential varies in space according to the relation $V=3x+4y.$ A particle of mass $0.1kg$ starts from rest from point $(2,3.2)$ under the influence of this field. The charge on the particle is $+1\mu C.$ Assume V and $(x,y)$ are in S.I. units

The component of electric field in the y - direction $\left(E_y\right)$ is

At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the ay in this situation?

How much water should be filled in a container 21 cm in height, so that it appears half filled when viewed from the top of the container (given that ${}^a{\mu }_w=\frac{4}{3}$

In the pulley arrangement shown in figure, pulley $P_2$ is movable. Assuming the coefficient of friction between the block having mass $m$ and the surface is $\mu$, find the maximum value of $M$ for which $m$ is at rest.

A 4 kg block is tied at one end of a massless belt as shown. The belt can slide on table. A 6 kg block is kept on the belt. The coefficient of friction between belt and table (${\mu }_1$) and between 6 kg block and belt (${\mu }_2$) is same and equal to 0.2. The system is released from rest. Answer the following questions: (Take g = 10 $m/s^2$)

Find the acceleration of 4 kg block

A
particle of mass m and
charge (−q)
enters the region between the two charged plates initially moving
along x-axis
with speed vx (like
particle 1 in Fig. 1.33). The length of plate is L
and an uniform electric field E
is maintained between the plates.
Show that the vertical deflection of the particle at the far edge of
the plate is qEL²/
(2m).

Compare
this motion with motion of a projectile in gravitational field
discussed in Section 4.10 of Class XI Textbook of Physics.

In a metre bridge, the null point is found to be at distance of 33.33 cm from left end $A$. The resistance connected in right gap is $12\Omega$. What is unknown resistance in left gap?

Which of the following remains unchanged when the sound wave travels from air to water?

A wire of length $l$, mass $m$ and resistance $R$ slide without any friction down the parallel conducting rails of negligible resistance. The rails are connected to each other at the bottom by a rail of negligible resistance which is parallel to the wire . The wire and rail forms a closed rectangular conducting loop. The plane of the rails makes an angle $\theta$ with the horizontal and a uniform magnetic field $B$ which exists throughout the region. Find the steady velocity of the wire.

If for a given angle of projection, the horizontal range is doubled, the time of flight becomes

An arrangement of pulley, string and blocks is shown in figure. Given $m_1=4\text{kg},m_2=2\text{kg}$ and $m_3=4\text{kg}$. All surfaces are frictionless, string and pulleys are massless. Find the acceleration of block $m_1$. Assume $g=10{\text{m/s}}^2$.

If the attraction force between two bodies separated by R is F, then find the force between them at distance (R+d).

A beam of light consisting of two wavelengths $420\text{nm}$ and $540\text{nm}$ falls on two metals $1$ and $2$ of work functions $4.0\text{eV}$ and $2.5\text{eV}$ respectively. If the intensities of the two wavelengths are equal, which of the graphs shown in figure represents the variation of photoelectric current $\left(i\right)$ with voltage $\left(V\right)$ is correct?

[Take $hc=1240\text{eV (nm)}$ ]

The initial capacitance of a parallel plate capacitor with air as a medium is $C_0$. After introducing a conducting sheet of thickness $\frac{d}{6}$, where $d$ is the separation between the metal plates, the capacitance becomes $C$. Then $\frac{C}{C_0}$ is

Two particles of masses $1\text{kg}$ and $2\text{kg}$ are located at $x=$$0\text{m}$ and $x=3\text{m}$. The position of their centre of mass (with respect to mass $1\text{kg}$) is

According to the sign convention used in ray optics, the origin for object distance measurement is

State two precautions that you must take when switching on an electric circuit.

A $20\text{kg}$ block is initially at rest on a rough horizontal surface. A horizontal force of $75\text{N}$ is required to set the block in motion. After it is in motion, a horizontal force of $60\text{N}$ is required to keep the block moving with constant speed. The coefficient of static friction is