List of practice Questions

A point particle of charge \( Q \) is located at \( P \) along the axis of an electric dipole 1 at a distance \( r \) as shown in the figure. The point \( P \) is also on the equatorial plane of a second electric dipole 2 at a distance \( r \). The dipoles are made of opposite charge \( q \) separated by a distance \( 2a \). For the charge particle at \( P \) not to experience any net force, which of the following correctly describes the situation?

Given below are two statements:
Statement-I: The hot water flows faster than cold water.
Statement-II: Soap water has higher surface tension as compared to fresh water.
In the light of the above statements, choose the correct answer from the options given below:

Identify the valid statements relevant to the given circuit at the instant when the key is closed.

\( \text{A} \): There will be no current through resistor R.
\( \text{B} \): There will be maximum current in the connecting wires.
\( \text{C} \): Potential difference between the capacitor plates A and B is minimum.
\( \text{D} \): Charge on the capacitor plates is minimum.
Choose the correct answer from the options given below:

Consider a circular disc of radius 20 cm with center located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of the center of mass of the residual or remaining disc from the origin will be:

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is \( P_1 \). The reading of the pressure gauge falls to \( P_2 \) when the valve is opened. The speed of water flowing in the pipe is proportional to:

A circular disk of radius \( R \) meter and mass \( M \) kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that \( \theta(t) = 5t^2 - 8t \), where \( \theta(t) \) is the angular position of the rotating disk as a function of time \( t \). How much power is delivered by the applied torque, when \( t = 2 \) s?

Water of mass \( m \) gram is slowly heated to increase the temperature from \( T_1 \) to \( T_2 \). The change in entropy of the water, given specific heat of water is \( 1 \, \text{J} \, \text{kg}^{-1} \, \text{K}^{-1} \), is:

Using the given P-V diagram, the work done by an ideal gas along the path ABCD is: \includegraphics[]{43.PNG}

What is the current through the battery in the circuit shown below? \includegraphics[]{41.PNG}

Two point charges \( -4 \, \mu C \) and \( 4 \, \mu C \), constituting an electric dipole, are placed at \( (-9, 0, 0) \, \text{cm \) and \( (9, 0, 0) \, \text{cm} \) in a uniform electric field of strength \( 10^4 \, \text{N/C} \). The work done on the dipole in rotating it from the equilibrium through \( 180^\circ \) is:}

In a series LCR circuit, a resistor of \( 300 \, \Omega \), a capacitor of \( 25 \, \text{nF} \), and an inductor of \( 100 \, \text{mH} \) are used. For maximum current in the circuit, the angular frequency of the AC source is -----\( \times 10^4 \) radians s\(^{-1}\).

A satellite of mass \( \frac{M}{2} \) is revolving around Earth in a circular orbit at a height of \( \frac{R}{3} \) from the Earth's surface. The angular momentum of the satellite is \( M \sqrt{\frac{GM R}{x}} \). The value of \( x \) is:

The energy of a system is given as \( E(t) = \alpha e^{-\beta t \), where \( t \) is the time and \( \beta = 0.3 \, \text{s}^{-1} \). The errors in the measurement of \( \alpha \) and \( t \) are 1.2 percent and 1.6 percent, respectively. At \( t = 5 \) s, the maximum percentage error in the energy is:}

The equation of a transverse wave travelling along a string is \( y(x, t) = 4.0 \sin \left( 20 \times 10^{-3} x + 600t \right) \) mm, where \( x \) is in mm and \( t \) is in seconds. The velocity of the wave is:

A ball having kinetic energy \( KE \), is projected at an angle of \( 60^\circ \) from the horizontal. What will be the kinetic energy of the ball at the highest point of its flight?