In a series LCR circuit, resistance R = 10 Ω and the impedance Z = 20 Ω . The phase difference between the current and the voltage is
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A system consists of two identical particles one particle is at rest and the other particle has an acceleration 'a'. The centre of mass of the system has an acceleration of
A small solid cylinder rolls up along a curved surface (fig.) with an initial velocity v. It will ascend up to a height ‘h’ equal to
A bullet of mass m is fired into a block of wood of mass M which hangs on the end of a pendulum and gets embedded in it. When the bullet strikes the wooden block, the pendulum starts to swing with a maximum rise R. The velocity of the bullet is given by
The electrical resistance of a mercury column in a cylindrical container is R. When the same mercury is poured into another cylindrical container twice the radius of cross-section, the resistance of mercury column now is
An electric dipole consists of two opposite charges of magnitude ± q seperated by 2a. When the dipole is placed in uniform electric field E, to have minimum potential energy, then dipole moment p makes which the following angle with E
The acceleration due to gravity at a height 1/10th of the radius of the earth above the earth's surface is 8.2 m-s⁻2. Its value at a point at the same distance below the surface of the earth is
A galvanometer having a resistance of 50 Ω gives a full scale deflection for a current of 0.05A. The length in meter of a resistance wire of area of cross section 2.97 x 10 − 3 c m 2 that can be used to convert the galvanometer into an ammeter which can be read a maximum of 5A current is [specific resistance of the wire = 5 x 10−7 c m 2 Ω − m ]
The moment of inertia of a uniform thin rod of length L and mass M about an axis passing through a point at a distance of L/3 from one of its ends and perpendicular to the rod is
The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity ν₀. the distance travelled by the particle in time t will be
A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is
A stone of mass 1 kg tied of the end of a 1 m long string, is whirled in a horizontal circle, with a uniform angular velocity of 2 rad-s⁻1. Tension of the string is
Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along x and y-axis. If the two amplitudes are equal and the phase difference is π/2, the resultant motion will be
Range of a projectile is R, when the angle of projection is 30o. Then, the value of the other angle of projection for the same range is