Assertion: When a simple pendulum is made to oscillate on the surface of moon, its time period increase.

Reason: Moon is much smaller compared to earth.

1. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
2. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
3. If the assertion is true but the reason is false
4. If both the assertion and reason are false

Assertion: When a simple pendulum is made to oscillate on the surface of moon, its time period increase.

Reason: Moon is much smaller compared to earth.

The average velocity of a particle executing SHM in one complete vibration is:
1. zero
2. \(\dfrac{A \omega}{2}\)
3. \(A \omega\)
4. \(\dfrac{A \left(\omega\right)^{2}}{2}\)

Two pendulums (with the same angular amplitudes) of time periods \(3~\text{s}\) and \(7~\text{s}\) respectively start oscillating simultaneously from two opposite extreme positions with the same angular amplitudes. After how much time they will be in phase?
1. \(\dfrac{21}{8}~\text{s}\)

2. \(\dfrac{21}{4}~\text{s}\)

3. \(\dfrac{21}{2}~\text{s}\)

4. \(\dfrac{21}{10}~\text{s}\)

A rectangular block of mass m and area of cross-section A floats in a liquid of density ρ. If it is given a small vertical displacement from equilibrium, it undergoes oscillation with a time period T. Then:
1. $T\propto \sqrt{\rho }$
2. $T\propto \frac{1}{\sqrt{A}}$
3. $T\propto \frac{1}{\rho }$
4. $T\propto \frac{1}{\sqrt{m}}$

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:
1. 0.5$\mathrm{\pi }$
2. $\mathrm{\pi }$
3. 0.707$\mathrm{\pi }$
4. zero

A mass of \(2.0\) kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes a simple harmonic motion. The spring constant is \(200\) N/m. What should be the minimum amplitude of the motion, so that the mass gets detached from the pan? 
(Take \(g=10\) m/s²) 
                

A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:
1. $\frac{\mathrm{T}}{4}$
2. $\frac{\mathrm{T}}{8}$
3. $\frac{\mathrm{T}}{12}$
4. $\frac{\mathrm{T}}{2}$