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Water falls from a height of $60\text{ m}$ at the rate of $15\text{ kg/s}$ to operate a turbine. The losses due to frictional force are $10\%$ of the input energy. How much power is generated by the turbine? ($g = 10\text{ m/s}^2$)
A dipole is placed in an electric field as shown. In which direction will it move?
The number of photons per second on an average emitted by the source of monochromatic light of wavelength $600\text{ nm}$, when it delivers the power of $3.3 \times 10^{-3}\text{ watt}$ will be ($h = 6.6 \times 10^{-34}\text{ J s}$)
A series LCR circuit containing $5.0\text{ H}$ inductor, $80\text{ }\mu\text{F}$ capacitor and $40\text{ }\Omega$ resistor is connected to $230\text{ V}$ variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be
A particular station of All India Radio, New Delhi broadcasts on a frequency of 1,368 kHz (kilohertz). The wavelength of the electromagnetic radiation emitted by the transmitter is : [speed of light $c = 3.0 \times 10^8 \text{ ms}^{-1}$]
A uniform conducting wire of length $12a$ and resistance '$R$' is wound up as a current carrying coil in the shape of, (i) an equilateral triangle of side '$a$'. (ii) a square of side '$a$'. The magnetic dipole moments of the coil in each case respectively are
A square loop of side $1\text{ m}$ and resistance $1\text{ }\Omega$ is placed in a magnetic field of $0.5\text{ T}$. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is
Match List-I with List-II<br><br>Choose the correct answer from the options given below
Plane angle and solid angle have
Two objects of mass $10\text{ kg}$ and $20\text{ kg}$ respectively are connected to the two ends of a rigid rod of length $10\text{ m}$ with negligible mass. The distance of the center of mass of the system from the $10\text{ kg}$ mass is
The energy that will be ideally radiated by a $100\text{ kW}$ transmitter in $1\text{ hour}$ is
A body of mass $60\text{ g}$ experiences a gravitational force of $3.0\text{ N}$, when placed at a particular point. The magnitude of the gravitational field intensity at that point is
A long solenoid of radius $1\text{ m}$ has $100\text{ turns per mm}$. If $1\text{ A}$ current flows in the solenoid, the magnetic field strength at the centre of the solenoid is
Given below are two statements: Statement I: Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only. Statement II: Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a vector source, Idl while the latter being produced by a scalar source, q. In light of above statements choose the most appropriate answer from the options given below:
Two hollow conducting spheres of radii $R_1$ and $R_2$ ($R_1 >> R_2$) have equal charges. The potential would be
A light ray falls on a glass surface of refractive index $\sqrt{3}$, at an angle $60^{\circ}$. The angle between the refracted and reflected rays would be
The ratio of the distances travelled by a freely falling body in the $1^{\text{st}}$, $2^{\text{nd}}$, $3^{\text{rd}}$ and $4^{\text{th}}$ second
If $\oint_s \vec{E} \cdot d\vec{S} = 0$ over a surface, then
A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is
Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is: