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A circular platform is mounted on a frictionless vertical axle. Its radius $R=2\text{ m}$ and moment of inertia about the axle is $200\text{ kg m}^2$. It is initially at rest. A $50\text{ kg}$ man stands on the edge of the platform and begins to walk along the edge at the speed of $1\text{ ms}^{-1}$ relative to the ground. Time taken by the man to complete one revolution is:
The driver of a car travelling at a speed of $30 \text{ m/s}$ towards a hill sounds a horn of frequency $600 \text{ Hz}$. If the velocity of sound in air is $330 \text{ m/s}$, the frequency of reflected sound as heard by the driver is:
The EM wave with the shortest wavelength among the following is:
A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is $\vec{F}$, the net force on the remaining three arms of the loop is
Two equally charged, identical metal spheres A and B repel each other with a force $F$. The spheres are kept fixed with a distance $r$ between them. A third identical, but uncharged sphere C is brought in contact with A, then brought in contact with B, and finally placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is:
The acceleration of a particle is increasing linearly with time $t$ as $bt$. The particle starts from the origin with an initial velocity of $v_0$. The distance travelled by the particle in time $t$ will be:
Young’s double-slit experiment is first performed in air and then in a medium other than air. It is found that the $8^{\text{th}}$ bright fringe in the medium lies where the $5^{\text{th}}$ dark fringe lies in the air. The refractive index of the medium is nearly:
The figure given below shows the displacement and time, $(x-t)$ graph of a particle moving along a straight line: The correct statement, about the motion of the particle, is:
A linear aperture whose width is $0.02\text{ cm}$ is placed immediately in front of a lens of focal length $60\text{ cm}$. The aperture is illuminated normally by a parallel beam of wavelength $5 \times 10^{-5}\text{ cm}$. The distance of the first dark band of the diffraction pattern from the centre of the screen is
Unpolarised light is incident from the air on a plane surface of a material of refractive index $\mu$. At a particular angle of incidence $i$, it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?
A beam of cathode rays is subjected to crossed Electric (E) and magnetic fields (B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by:
In Young's double-slit experiment, the separation $d$ between the slits is $2 \text{ mm}$, the wavelength $\lambda$ of the light used is $5896 \text{ \AA}$ and distance $D$ between the screen and slits is $100 \text{ cm}$. It is found that the angular width of the fringes is $0.20^{\circ}$. To increase the fringe angular width to $0.21^{\circ}$ (with same $\lambda$ and $D$) the separation between the slits needs to be changed to:
A parallel beam of fast-moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct?
Under the influence of a uniform magnetic field, a charged particle moves with constant speed v in a circle of radius R. The time period of rotation of the particle -
A galvanometer having a coil resistance of 60 $\Omega$ shows full scale deflection when a current of 1.0 A passes through it. It can be converted into an ammeter to read currents upto 5.0 A by
The unit of reduction factor of the tangent galvanometer is:
A galvanometer of resistance 50 Ω is connected to a battery of 3 V along with a resistance of 2950 Ω in series. A full-scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be:
When a 12 \Omega resistor is connected in parallel with a moving coil galvanometer, its deflection reduces from 50 divisions to 10 divisions. What will be the resistance of the galvanometer?
Eight dipoles of charges of magnitude $e$ are placed inside a cube. The total electric flux coming out of the cube will be:
The net resistance of a voltmeter should be large to ensure that: