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The instantaneous values of alternating current and voltages in a circuit are given as $i = \frac{1}{\sqrt{2}} \sin(100\pi t)$ ampere and $e = \frac{1}{\sqrt{2}} \sin(100\pi t + \pi/3)$ volt. The average power in Watts consumed in the circuit is:
A solid sphere is rotating about a diameter at an angular velocity $\omega$. If it cools so that its radius reduces to $\frac{1}{n}$ of its original value, its angular velocity becomes:
The peak voltage of the AC source is equal to:
An AC source is connected to a capacitor C. Due to a decrease in its operating frequency:
A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass $m$ is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period:
A black body is at a temperature of $5760\text{ K}$. The energy of radiation emitted by the body at a wavelength of $250\text{ nm}$ is $U_1$, at a wavelength of $500\text{ nm}$ is $U_2$ and that at $1000\text{ nm}$ is $U_3$. Given Wien's constant $b=2.88 \times 10^6\text{ nm K}$, which of the following is correct?
An AC source is connected to the given circuit. The value of $\phi$ will be:
The M.I. of a body about the given axis is $1.2 \text{ kg m}^2$. Initially, the body is at rest. In order to have a rotational kinetic energy of 1500 J, an angular acceleration of $25 \text{ rad/s}^2$ must be applied about that axis for a duration of:
In the given circuit, the reading of voltmeter V1 and V2 are 300 V each. The reading of the voltmeter V3 and ammeter A are respectively:
L, C and R represent the value of inductance, capacitance, and resistance, respectively. The factor which has the same dimensions as that of the inverse of the resonance frequency is:
Consider a system of two particles having masses $m_1$ and $m_2$. If the particle of mass $m_1$ is pushed towards the centre of mass of particles through a distance $d$, by what distance would the particle of the mass $m_2$ move so as to keep the centre of mass of particles at the original position?
From a circular disc of radius $R$ and mass $9M$, a small disc of mass $M$ and radius $R/3$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is:
A transformer is used to light a 100 W and 110 V lamp from a 220 V main. If the main current is 0.5 A, the efficiency of the transformer is approximately:
The energy of ground electronic state of hydrogen atom is -13.6 eV. The energy of the first excited state will be:
A solid sphere, disc, and solid cylinder all of the same mass and made up of the same material are allowed to roll down (from rest) on an inclined plane, then:
The photon radiated from hydrogen corresponding to the second line of Lyman series is absorbed by a hydrogen-like atom X in the second excited state. As a result the hydrogen-like atom X makes a transition to nth orbit. Then:
Three objects, $A$ (a solid sphere), $B$ (a thin circular disk) and $C$ (a circular ring), each have the same mass $M$ and radius $R$. They all spin with the same angular speed about their own symmetry axes. The amount of work ($W$) required to bring them to rest, would satisfy the relation:
The total energy of an electron in the first excited state of hydrogen is about -3.4 eV. Its kinetic energy in this state is:
Point masses $m_1$ and $m_2$ are placed at the opposite ends of a rigid rod of length $L$ and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $\omega_0$ is minimum, is given by:
A disc and a solid sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?