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A roller coaster is designed such that riders experience "weightlessness" as they go around the top of a hill whose radius of curvature is $20 \text{ m}$. The speed of the car at the top of the hill is between:
The coefficient of static friction, $\mu_s$, between block A of mass 2 kg and the table as shown in the figure is 0.2. What would be the maximum mass value of block B so that the two blocks do not move? The string and the pulley are assumed to be smooth and massless. ($g = 10 \text{ m/s}^2$)
The voltage reading on the voltmeter V in the circuit shown below will be:
In an electrical circuit R, L, C, and an AC voltage source are all connected in series. When L is removed from the circuit, the phase difference between the voltage and the current in the circuit is π/3. If instead, C is removed from the circuit, the phase difference is again π/3. The power factor of the circuit is:
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:
Four charges each equal to $Q$ are placed at the four corners of a square and a charge $q$ is placed at the centre of the square. If the system is in equilibrium, then the value of $q$ is:
An inductor $20 \text{ mH}$, a capacitor $50 \mu\text{F}$, and a resistor $40 \, \Omega$ are connected in series across a source of emf $V = 10\sin(340t)$. The power loss in the AC circuit is:
A balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?
Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is:
Given below are two statements: Statement I: In an AC circuit, the current through a capacitor leads the voltage across it. Statement II: In AC circuits containing pure capacitance only, the phase difference between the current and the voltage is $\pi$.
A 220V input is supplied to a transformer. The output circuit draws a current of 2.0A at 440V. If the efficiency of the transformer is 80%, the current drawn by the primary windings of the transformer is
A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40 Ω resistor is connected to 230 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:
In which of the following cases, a force will not be required to keep the particle in the given motion?
A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity $\omega_0$. If the length of the string and angular velocity are doubled, the tension in the string which was initially $T_0$ is now:
Match List-I with List-II. List-I (Spectral Lines of Hydrogen for transitions from) A. n₂=3 to n₁=2 B. n₂=4 to n₁=2 C. n₂=5 to n₁=2 D. n₂=6 to n₁=2 List-II (Wavelength (nm)) I. 410.2 II. 434.1 III. 656.3 IV. 486.1 Choose the correct answer from the options given below:
The mass of a lift is $2000 \text{ kg}$. When the tension in the supporting cable is $28000 \text{ N}$, its acceleration is:
Two coils of self-inductance $2 \text{ mH}$ and $8 \text{ mH}$ are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:
A $1 \text{ kg}$ object strikes a wall with velocity $1 \text{ ms}^{-1}$ at an angle of $60^\circ$ with the wall and reflects at the same angle. If it remains in contact with the wall for $0.1 \text{ s}$, then the force exerted on the wall is:
Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication?
A 10 $\mu$F capacitor is connected to a 210 V, 50 Hz source. The peak current in the circuit is nearly ($\pi = 3.14$):