Motion Test - 6

According to the question the correct option will be ‘D’ because Simple harmonic motion is a special type of periodic motion, in which a particle moves to and fro repeatedly about a mean position. So, motion of oscillating liquid column in U-tube is simple harmonic.

According to the question the correct option will be ‘B’ because Newton's first law states that; "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force”. Thus, body continues in its state of rest as there is no external force on it,

So, option B is correct.

Let the General equation of SHM x = A sin(ωt+ϕ), Where x is displacement from the mid position and A is amplitude of SHM.

⇒ −A ≤ x ≤ A,

Now in the question, $\frac{\mathrm{\pi }}{3}=\frac{\mathrm{\pi }}{6}=\sin \left(wt\right)$

Since instantaneous angular displacement is more than the angular amplitude so this equation of SHM is incorrect.

According to the question the correct option will be ‘B’ because Impulse:- It is defined as a change in momentum due to force in small time.

Mathematically,

From Newton's law,

F=$\frac{∆p}{∆t}$

Impulse, I = F × Δt = ΔP

The correct option is B.

$\sqrt{a^2-b{v}^2}$According to the question the correct option will be ‘D’ because Relation (d) which is x=$\sqrt{a-b{v}^2}$correclty represents the SHM because , velocity

V=$\sqrt[w]{a^2-x^2}$

or  x=$\sqrt{a^2-v^2/{\omega }^2}$

or \(x=\sqrt{a-b v^{2}}\)
where,b=$\frac{1}{{\omega }^2}$

According to the question the correct option will be ‘A’ because a book lying on the table is at rest.

Since no net external force is acting on the book in this state and so it is not capable of moving the book.

Option A is correct.

According to the question the correct option will be ‘A’ because When tuning is on a table, a large sound is heard. It creates the forced vibration of a table. As a result of a sound also comes out from the table which has much larger intensity.

According to the question the correct option will be ‘A’ because All oscillatory is periodic, as in all oscillatory motion particle repeats its position after a certain interval of time.

According to the question the correct option will be ‘B’ because the motion of the hand is an oscillatory motion, as the motion repeats in a finite interval of time and the to and fro motion happens in a given time period

As the hand moves to one extreme, a restoring force acts in the opposite direction to move it back to the mean and then to the other extreme position. Thus, the bye-bye gesture of the hand is an oscillating motion

The correct option is (B)

According to the question the correct option will be ‘B’ because a body is said to be at rest if it remains in one position for a long time.

All the three object are in any oscillatory motion w r t to earth as frame of reference. But study table is at rest.

So study table is odd one out of the four objects.

According to the question the correct option will be ‘B’ because the equation for displacement in oscillation is x = A sin (ωt+α)

Since x is a sine function of time, the graph is sinusoidal in nature.

\(x=a \sin ^{2} \omega t=a\left(\frac{1-\cos 2 \omega t}{2}\right)\)     \(\left(\because \cos 2 \theta=1-2 \sin ^{2} \theta\right)\)

\(=\frac{a}{2}-\frac{a \cos 2 \omega t}{2}\)

\(\therefore \quad\) Velocity, \(v=\frac{d x}{d t}=\frac{2 \omega a \sin 2 \omega t}{2}=\omega a \sin 2 \omega t\)

Acceleration, \(a=\frac{d v}{d t}=2 \omega^{2} a \cos 2 \omega t\)

For the given displacement \(x\) a \(\sin ^{2} w / t\)

Hence, the motion of the particle is non simple harmonic motion.

According to the question the correct option will be ‘C’ because Flapping of wings was oscillatory, since it constitutes to and fro motion, while birds motion along a circle is periodic

Thus the correct option is (c)

 According to the question the correct option will be ‘A’ because for a motion to be SHM, it has to be small amplitude and the acceleration is proportional to the displacement of the particle and directed against its displacement. Here the acceleration has centripetal and tangential components (here zero since uniform circular motion) but has no variation with particle displacement hence can be oscillatory but not in SHM.