Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Knowing the initial position \( x_0 \) and initial momentum \( p_0 \) is enough to determine the position and momentum at any time \( t \) for a simple harmonic motion with a given angular frequency \( \omega \). Reason (R): The amplitude and phase can be expressed in terms of \( x_0 \) and \( p_0 \). In the light of the above statements, choose the correct answer from the options given below:
In the circuit shown, assuming the threshold voltage of the diode is negligibly small, then the voltage \( V_{AB} \) is correctly represented by:
Match List - I with List - II.
Choose the correct answer from the options given below:
An infinite wire has a circular bend of radius \( a \), and carrying a current \( I \) as shown in the figure. The magnitude of the magnetic field at the origin \( O \) of the arc is given by:
A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per meter in the solenoid is …………
The increase in pressure required to decrease the volume of a water sample by 0.2percentage is \( P \times 10^5 \, \text{Nm}^{-2} \). Bulk modulus of water is \( 2.15 \times 10^9 \, \text{Nm}^{-2} \). The value of \( P \) is ………..
A string of length \( L \) is fixed at one end and carries a mass of \( M \) at the other end. The mass makes \( \frac{3}{\pi} \) rotations per second about the vertical axis passing through the end of the string as shown. The tension in the string is \_\_\_\_ ML.
In photoelectric effect, the stopping potential \( V_0 \) vs frequency \( \nu \) curve is plotted. \( h \) is the Planck's constant and \( \phi_0 \) is the work function of metal. (A) \( V_0 \) vs \( \nu \) is linear. (B) The slope of \( V_0 \) vs \( \nu \) curve is \( \frac{\phi_0}{h} \). (C) \( h \) constant is related to the slope of \( V_0 \) vs \( \nu \) line. (D) The value of electric charge of electron is not required to determine \( h \) using the \( V_0 \) vs \( \nu \) curve. (E) The work function can be estimated without knowing the value of \( h \). \text{Choose the correct answer from the options given below:}
Arrange the following in the ascending order of wavelength (\( \lambda \)): (A) Microwaves (\( \lambda_1 \)) (B) Ultraviolet rays (\( \lambda_2 \)) (C) Infrared rays (\( \lambda_3 \)) (D) X-rays (\( \lambda_4 \)) \text{Choose the most appropriate answer from the options given below:}
The output of the circuit is low (zero) for:
(A) \( X = 0, Y = 0 \) (B) \( X = 0, Y = 1 \) (C) \( X = 1, Y = 0 \) (D) \( X = 1, Y = 1 \)Choose the correct answer from the options given below:
N equally spaced charges each of value \( q \) are placed on a circle of radius \( R \). The circle rotates about its axis with an angular velocity \( \omega \) as shown in the figure. A bigger Amperian loop \( B \) encloses the whole circle, whereas a smaller Amperian loop \( A \) encloses a small segment. The difference between enclosed currents, \( I_B - I_A \) for the given Amperian loops is: