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In a series LCR circuit, the inductance $L$ is 10 mH, capacitance $C$ is 1 $\mu$F and resistance $R$ is 100 $\Omega$. The frequency at which resonance occurs is
The reaction can be classified as:
A couple produces:
The temperature of a gas is $-50^{\circ}$C. To what temperature the gas should be heated so that the rms speed is increased by 3 times?
Two particles that are initially at rest, move towards each other under the action of their mutual attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of the centre of mass of the system will be:
A disc of radius $2 \text{ m}$ and mass $100 \text{ kg}$ rolls on a horizontal floor. Its centre of mass has a speed of $20 \text{ cm/s}$. How much work is needed to stop it?
A particle starting from rest moves in a circle of radius $r$. It attains a velocity of $v_0 \text{ m/s}$ on completion of $n$ rounds. Its angular acceleration will be:
A particle of mass $5m$ at rest suddenly breaks on its own into three fragments. Two fragments of mass $m$ each move along mutually perpendicular directions with speed $v$ each. The energy released during the process is:
A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?
Two particles of mass $5 \text{ kg}$ and $10 \text{ kg}$ respectively are attached to the two ends of a rigid rod of length $1 \text{ m}$ with negligible mass. The centre of mass of the system from the $5 \text{ kg}$ particle is nearly at a distance of:
In an orbital motion, the angular momentum vector is:
Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $D_1$ has $2\text{ kg}$ mass and $0.2\text{ m}$ radius and initial angular velocity of $50\text{ rad s}^{-1}$. Disc $D_2$ has $4\text{ kg}$ mass, $0.1\text{ m}$ radius and initial angular velocity of $200\text{ rad s}^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in $\text{rad s}^{-1}$) of the system is
Two rotating bodies $A$ and $B$ of masses $m$ and $2m$ with moments of inertia $I_A$ and $I_B$ ($I_B > I_A$) have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momenta respectively, then:
A uniform rod AB of length $l$ and mass $m$ is free to rotate about point A. The rod is released from rest in horizontal position. Given that the moment of inertia of the rod about A is $\frac{ml^2}{3}$, the initial angular acceleration of the rod will be:
Which of the following will not be affected if the radius of the sphere is increased while keeping mass constant?
In uniform circular motion:
If rotational kinetic energy is $50\%$ of translational kinetic energy, then the body is:
The increase in the width of the depletion region in a p-n junction diode is due to :
A solid cylinder of mass $50 \text{ kg}$ and radius $0.5 \text{ m}$ is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of $2 \text{ rev/s}^2$ is:
By which method was a new breed 'Hisardale' of sheep formed by using Bikaneri ewes and Marino rams?