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A concave mirror forms a real image of a point source lying on the optical axis at a distance of $50\text{cm}$ from the mirror. The focal length of the mirror is $25\text{cm}$. The mirror is cut into two equal parts and each of the two halves are rotated about $S$ by ${90}^{\circ }$, one in anticlockwise and other in clockwise with reference to the original position, then the distance between the two images formed by each part will be

A dip needle lies initially in the magnetic meridian when it shows an angle of dip $\theta$ at a place. The dip circle is rotated through an angle $x$ in the horizontal plane and then it shows an angle of dip $\theta \text{'}.$ Then $\frac{\tan \theta \text{'}}{\tan \theta }$ is

A particle executing simple harmonic motion, obeys the equation for its position as $x=6\sin [4t-\frac{\pi }{6}]cm$.
The velocity of the particle when its position is $3cm$ is

A square plate is hinged as shown in figure and it is held stationary by means of a light thread as shown in figure. Then find out the force exerted by the hinge.

A 0.5 kg ball is thrown horizontally from point A with velocity $V_A=2m/s$. It strikes the smooth inclined plane and bounces. Take coefficient of restitution e =0.6 and $g=10m/s^2$

The speed at which it bounces from the plane is

Which of the following processes is an iso-entropic process?

The figure shows a solenoid carrying time varying current $I=I_{0}t$. On the axis of this solenoid a ring has been placed. The mutual inductance of the ring and the solenoid is $M$ and the self inductance of the ring is $L$. If the resistance of the ring is $R$ then the maximum current which can flow through the ring is equal to

Why is the net force on a current carrying solenoid in uniform magnetic field equal to zero

A car is moving on a circular level road of radius of curvature $300\text{m}$. If the coefficient of friction is $0.5$ and taking $g=10{\text{m/s}}^2$, the maximum speed the car can have (in $\text{km/hr}$) is

An ideal gas at ${27}^{\circ }\text{C}$ is compressed adiabatically to $\frac{4}{9}$ of its original volume. If $\gamma =1.5$, then the final temperature of the gas is

If $x,v$ and $a$ denotes the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T$. Then which of the following does not change with time?

A ball is dropped onto a fixed horizontal surface from height h₀. The coefficient of restitution is ‘e’. The total distance ‘D’ travelled by ball before it comes to rest on the surface.

Two plane mirrors A and B are aligned parallel to each as shown in the figure. A light ray is incident at an angle of ${30}^{\circ }$ at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is

A solid cylinder of radius R & length 3R is made of a material having density $\rho$. Now two hemispheres each of radius R is removed from two ends of cylinder as shown in figure. Determine the moment of inertia of this object about axis of cylinder

Which amongst the following graphs represents the V-T graph shown in the figure?

A particle of mass $0.01\text{kg}$ travels with a velocity given by $4\hat{i}+16\hat{k}{\text{ms}}^{-1}$. After sometime, its velocity becomes $8\hat{i}+20\hat{j}{\text{ms}}^{-1}$. The work done on particle during this interval of time is

A magnetic field exists in a smoke chamber shown perpendicular to the plane of paper (either upwards or downwards). A beam coming out of a radioactive material [consisting of $\alpha ,{\beta }^{-},\gamma$ particles, proton $\left(H^{+}\right)$, Neutron] enters into the chamber through a fine hole, the four rays are named as $A,B,C$ and $D$.
[Assume $\alpha ,{\beta }^{-},$ Neutron and proton have nearly the same velocity.]
$\begin{array}{cccc}& \text{Column-I}& & \text{Column-II}\\ \text{(A)}& A& \text{(P)}& \alpha \\ \text{(B)}& B& \text{(Q)}& {\beta }^{-}\\ \text{(C)}& C& \text{(R)}& \gamma \\ \text{(D)}& D& \text{(S)}& H^{+}\\ & & \text{(T)}& \text{Neutron}\end{array}$
Which of the following option has the correct combination considering column-I and column-II.

A uniform rod of mass $m$ and length $l$ hinged at point $\text{H}$ can rotate in a vertical plane about a smooth horizontal axis. Find the force exerted by the hinge just after the rod is released from rest, from an initial position making an angle of ${37}^{\circ }$ with horizontal.

During the emission spectrum of electron in $H{e}^{+}$ ion, the electron on transition from same higher energy state drops to the ground state and first excited state emits two photon of ${\lambda }_1$=304 $A^{\circ }$ and ${\lambda }_2$=1085 $A^{\circ }$ respectively.The total number of photons emitted during the transition of electrons from highest excited to all lower energy level(Possible)

Two moles of helium $\left(He\right)$ are mixed with four moles of hydrogen $\left(H_2\right)$. The value of $\gamma$ of the mixture is

A uniform solid brass sphere is rotating with angular speed ${\omega }_0$ about a diameter. If its temperature is now increased by ${100}^{\circ }\text{C}$. What will be its new angular speed? (Given ${\alpha }_B=2.0\times {10}^{-5}{\text{per}}^{\circ }C$)

Can two isothermal curves cut each other

A cylindrical wire of length $0.1\text{m}$ has specific gravity $11$. What is the maximum diameter of the wire that can float on the surface of water, if surface tension of water is $0.07\text{N/m}$. (Take $g=10{\text{m/s}}^2$)

A system is shown in fig. Assume that the cylinder remains in contact with the two wedges. Then the velocity of cylinder is

A rod of mass $M$ is rotating with angular velocity ${}^{\prime }{\omega }^{\prime }$ about its central axis. Two particles of same mass$\left(M\right)$ lie near the axis. Find the angular velocity of the rod when particles reach at ends.

Can I have cbse board preparation notes of chapter ""electric potential and capacitance"" of physics... Please give me detailed notes....

If the wavelength of light is $4000\stackrel{\circ }{A}$, then the number of waves in 1 mm length will be

A wave is reflected from a rigid support. The change in phase on reflection will be

[MP PMT 1990; RPMT 2002]

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

Water rises to a height $h$ in a capillary tube of area of cross-section $a$. To what height will the water rise in a capillary tube of area of cross-section $4a$ ?

A hole of radius $r_1$ is made centrally in a uniform circular disc of thickness d and radius $r_2$. The inner surface (a cyclinder of length d and radiud $r_1$) is maintained at a temperature ${\theta }_1$ and the outer surface (a cylinder of length d and radius $r_2$) is maintained at a temperature ${\theta }_2({\theta }_4>{\theta }_2)$. The thermal conductivity of the material of the disc is K. Calculate the heat flowing per unit time through the disc.

1 amu when expressed as $1.66\times$ ${10}^{-x}$g ,x =?

The engine of a train sounds a whistle at frequency $\left(f\right)$. The frequency heard by a passenger is

A particle of mass $0.1\text{kg}$ is subjected to a force which varies with distance as shown. If it starts its journey from rest at $x=0$, then its velocity at $x=12\text{m}$ is

A block is kept on a horizontal table. The table is executing simple harmonic motion of time period T in the horizontal plane. The coefficient of static friction between the block and the table is $\mu$. The maximum amplitude of the table for which the block does not slip on the surface of the table is

The resonant frequency of a circuit is f. If the capacitance is made 16 times the initial values, then the resonant frequency will become

A particle of mass m was transferred from the centre of the base of a uniform hemisphere of mass M and radius R to infinity. How much work would be performed in this process by the gravitational force exerted on the particle by the hemisphere?

A wire PQRS carrying a current $I$ runs along three edges of a cube of side $l$ as shown. There exists a uniform magnetic field of magnitude $B$ along one of the sides of the cube. The magnitude of the force acting on the wire is

Two spherical vessel of equal volume, are connected by a n arrow tube. The apparatus contains an ideal gas at one atmosphere and 300K. Now if one vessel is immersed in a bath of constant temperature 600K and the other in a bath of constant temperature 300K. Then the common pressure will be

An aluminium rod having length $100\text{cm}$ is clamped at its middle point and set into longitudinal vibrations. Let the rod vibrate in its fundamental mode. The density of aluminium is $2600{\text{kg/m}}^3$ and its Young's modulus is $7.8\times {10}^{10}{\text{N/m}}^2.$ The frequency of the sound produced is

If Rohit moves along a circular path from point $A(0,0)$ as shown in the figure and reaches diametrically opposite point $B(5,0)$, what is his displacement vector? Given: radius of circle is $2.5$ unit.

Four point charges $q_A=\mu c,q_B=-5\mu c{q}_c=2\mu cand{q}_D=-5\mu c$ are located at the corners of a square ABCD of side 10 cm. What is the force on the charge of 1 placed at the centre of the square.

An electron enters a region that contains a magnetic field directed into the page as shown in figure. The velocity vector of the electron makes an angle of ${30}^{\circ }$ with the +y axis. What is the direction of the magnetic force on the electron when it enters the field?

A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm. A charge $q=20\mu C$ is given to the inner sphere. Find the heat generated in the process when the inner sphere is connected to the shell by a conducting wire