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A $100 \, \Omega$ resistance and a capacitor of $100 \, \Omega$ reactance are connected in series across a $220$ V source. When the capacitor is $50\%$ charged, the peak value of the displacement current is:
A car of mass $1000 \text{ kg}$ negotiates a banked curve of radius $90 \text{ m}$ on a frictionless road. If the banking angle is $45^\circ$, the speed of the car is:
Hydrogen ($^1H$), Deuterium ($^2H$), singly ionised helium ($He^+$), and doubly ionised lithium ($Li^{2+}$) all have one electron around the nucleus. Consider an electron transition from n=2 to n=1. If the wavelengths of emitted radiations are $\lambda_1$, $\lambda_2$, $\lambda_3$, and $\lambda_4$ respectively, then approximately which one of the following is correct?
A $0.5 \text{ kg}$ ball moving with a speed of $12 \text{ m/s}$ strikes a hard wall at an angle of $30^{\circ}$ with the wall. It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for $0.25 \text{ s}$, the average force acting on the wall is:
A $5000 \text{ kg}$ rocket is set for vertical firing. The exhaust speed is $800 \text{ ms}^{-1}$. To give an initial upward acceleration of $20 \text{ ms}^{-2}$, the amount of gas ejected per second to supply the needed thrust will be ($g = 10 \text{ ms}^{-2}$)
A circuit when connected to an AC source of 12 V gives a current of 0.2 A. The same circuit when connected to a DC source of 12 V, gives a current of 0.4 A. The circuit is:
A car of mass $m$ is moving on a level circular track of radius $R$. If $\mu_s$ represents the static friction between the road and tyres of the car, then the maximum speed of the car in circular motion is given by:
A $40 \mu\text{F}$ capacitor is connected to a $200\text{ V}$, $50\text{ Hz}$ AC supply. The RMS value of the current in the circuit is, nearly:
Given below are two statements: Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their characteristic spectrum. In the light of the above statements, choose the most appropriate answer from the options given below:
What is the value of inductance L for which the current is maximum in a series LCR circuit with C = 10 μF and ω = 1000 s⁻¹?
Which one of the following statements is incorrect?
A coil of inductive reactance $31 \, \Omega$ has a resistance of $8 \, \Omega$. It is placed in series with a condenser of capacitive reactance $25 \, \Omega$. The combination is connected to an a.c. source of $110$ V. The power factor of the circuit is:
A series LCR circuit with inductance 10 H, capacitance 10 μF, and resistance 50 Ω is connected to an AC source of voltage $V = 200 \sin(100t)$ V. If the resonant frequency of the LCR circuit is $\nu_0$ and the frequency of the AC source is $\nu$, then:
Sand is being dropped on a conveyor belt at the rate of $M \text{ kg/s}$. The force necessary to keep the belt moving with a constant velocity of $v \text{ m/s}$ will be:
A ball of mass 150 g starts moving with an acceleration of 20 m/s² when hit by a force, which acts on it for 0.1 s. The impulsive force is:
A transistor-oscillator using a resonant circuit with an inductance L (of negligible resistance) and a capacitance C has a frequency f. If L is doubled and C is changed to 4C, the frequency will be:
A spring of force constant $k$ is cut into lengths of ratio $1:2:3$. They are connected in series and the new force constant is $k'$. If they are connected in parallel and force constant is $k''$, then $k':k''$ is:
A car of mass $1000 \text{ kg}$ negotiates a banked curve of radius $90 \text{ m}$ on a frictionless road. If the banking angle is $45^{\circ}$, the speed of the car is:
The mass of a lift is $2000 \text{ kg}$. When the tension in the supporting cable is $28000 \text{ N}$, then its acceleration is: (Take $g=10 \text{ m/s}^2$)
Two stones of masses $m$ and $2m$ are whirled in horizontal circles, the heavier one in a radius $r/2$ and the lighter one in the radius $r$. The tangential speed of lighter stone is $n$ times that of heavier stone when they experience the same centripetal forces. The value of $n$ is: