A particle moves in a circular path with a continuously increasing speed. Its motion is:
1. periodic
2. oscillatory
3. simple harmonic
4. none of them

The motion of a torsional pendulum is

(a) periodic

(b) oscillatory

(c) simple harmonic

(d) angular simple harmonic

Choose the correct option:

1. (a), (b) and (c)

2. (b), (c) and (d)

3. (a), (b) and (d)

4. All of these

Which of the following quantities are always negative in a simple harmonic motion?

(a) \(\vec{F} \cdot \vec{a}.\)

(b) \(\vec{v} \cdot \vec{r}.\)

(c) \(\vec{a} \cdot \vec{r}.\)

(d) \(\vec{F} \cdot \vec{r}\)

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. (d) and (e)

Which of the following quantities are always positive in a simple harmonic motion?

1. \(\vec{F} \cdot \vec{a}.\)

2. \(\vec{v} \cdot \vec{r}.\)

3. \(\vec{a} \cdot \vec{r}.\)

4. \(\vec{F} \cdot \vec{r}\)

Which of the following quantities are always zero in a simple harmonic motion?

Choose the correct option:

Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly above the tunnel. The motion of the particle as seen from the earth is:

(a) simple harmonic

(b) parabolic

(c) on a straight line

(d) periodic

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

For a particle executing simple harmonic motion, the acceleration is proportional to:
 

A particle moves in the X-Y plane according to the equation \(\vec{r}=(\vec{i}+2 \vec{j}) A \cos \omega t\).

The motion of the particle is:

(a) on a straight line

(b) on an ellipse

(c) periodic

(d) simple harmonic

Choose the correct option:

1. (a), (b) and (c)

2. (b), (c) and (d)

3. (a), (c) and (d)

4. All of these

A particle moves on the X-axis according to the equation \(x=x_{0} \sin ^{2} \omega t\). The motion is simple harmonic

1. with amplitude \(x_{0}\)

2. with amplitude \(2 x_{0}\)

3. with time period \(\frac{2 \pi}{\omega}\)

4. with time period \(\frac{\pi}{\omega}\)

In a simple harmonic motion:

1. the potential energy is always equal to the kinetic energy

2. the potential energy is never equal to the kinetic energy

3. the average potential energy in any time interval is equal to the average kinetic energy in that time interval

4. the average potential energy in one time period equal to the average kinetic energy in this period