The maximum velocity and the maximum acceleration of a body executing simple harmonic oscillator are 2 m/s and 4 m/s2 and Then angular velocity will be A. 3 rad/sec B. 0.5 rad/sec C. 1 rad/sec D. 2 rad/sec

Content Curator

The correct option is (D)

The maximum acceleration of a body executing simple harmonic motion of amplitude A and angular velocity ω is given by

a_max = ω²A

The maximum velocity of a body executing simple harmonic motion of amplitude A and angular velocity ω is given by

v_max = ωA

Taking the ratio of maximum acceleration to maximum velocity, we get

\(\frac{a_{max}}{v_{max}} = \frac{\omega^2A}{\omega A} = \omega\)

Hence, the angular velocity of the body is the ratio of maximum acceleration to maximum velocity

⇒ ω = \(\frac{a_{max}}{v_{max}}\)

Given in question,

Maximum acceleration of the body, a_max = 4 m/s²

Maximum velocity of the body, v_max = 2 m/s

Therefore, the angular velocity of the body is given by

ω = \(\frac{a_{max}}{v_{max}}\) = \(\frac{4}{2}\) = 2 rad/sec

Also Read:

Related Articles
Uniform Circular Motion	Banking of Roads	Newton’s third law of motion
Constant Acceleration	Frictional Force	Interaction of Forces & Effects of Force Interaction
Pseudo Force	Conservative Force	Equations of Motion by Graphical Method
Impulse Units	Unit of Mass	Differences between Acceleration and Velocity
Relative Velocity	Laws of Friction	Measuring Rate of Change Motion

CBSE CLASS XII Related Questions

1.
In the circuit, three ideal cells of e.m.f. \( V \), \( V \), and \( 2V \) are connected to a resistor of resistance \( R \), a capacitor of capacitance \( C \), and another resistor of resistance \( 2R \) as shown in the figure. In the steady state, find (i) the potential difference between P and Q, (ii) the potential difference across capacitor C.

View Solution

2.
The resistance of a wire at 25°C is 10.0 \( \Omega \). When heated to 125°C, its resistance becomes 10.5 \( \Omega \). Find (i) the temperature coefficient of resistance of the wire, and (ii) the resistance of the wire at 425°C.

View Solution

3.
Write the mathematical forms of three postulates of Bohr’s theory of the hydrogen atom. Using them prove that, for an electron revolving in the \( n \)-th orbit,
(a) the radius of the orbit is proportional to \( n^2 \), and
(b) the total energy of the atom is proportional to \( \frac{1}{n^2} \).

View Solution

4.
The electric field at a point in a region is given by \( \vec{E} = \alpha \frac{\hat{r}}{r^3} \), where \( \alpha \) is a constant and \( r \) is the distance of the point from the origin. The magnitude of potential of the point is:

\( \frac{\alpha}{r} \)
\( \frac{\alpha r^2}{2} \)
\( \frac{\alpha}{2r^2} \)
\( -\frac{\alpha}{r} \)

View Solution

5.
Three batteries E1, E2, and E3 of emfs and internal resistances (4 V, 2 \(\Omega\)), (2 V, 4 \(\Omega\)) and (6 V, 2 \(\Omega\)) respectively are connected as shown in the figure. Find the values of the currents passing through batteries E1, E2, and E3.

View Solution

6.
A current carrying circular loop of area A produces a magnetic field \( B \) at its centre. Show that the magnetic moment of the loop is \( \frac{2BA}{\mu_0} \sqrt{\frac{A}{\pi}} \).

View Solution

The maximum velocity and the maximum acceleration of a body executing simple harmonic oscillator are 2 m/s and 4 m/s2 and Then angular velocity will be A. 3 rad/sec B. 0.5 rad/sec C. 1 rad/sec D. 2 rad/sec

CBSE CLASS XII Related Questions

2.
The resistance of a wire at 25°C is 10.0 \( \Omega \). When heated to 125°C, its resistance becomes 10.5 \( \Omega \). Find (i) the temperature coefficient of resistance of the wire, and (ii) the resistance of the wire at 425°C.

4.
The electric field at a point in a region is given by \( \vec{E} = \alpha \frac{\hat{r}}{r^3} \), where \( \alpha \) is a constant and \( r \) is the distance of the point from the origin. The magnitude of potential of the point is:

5.
Three batteries E1, E2, and E3 of emfs and internal resistances (4 V, 2 \(\Omega\)), (2 V, 4 \(\Omega\)) and (6 V, 2 \(\Omega\)) respectively are connected as shown in the figure. Find the values of the currents passing through batteries E1, E2, and E3.

6.
A current carrying circular loop of area A produces a magnetic field \( B \) at its centre. Show that the magnetic moment of the loop is \( \frac{2BA}{\mu_0} \sqrt{\frac{A}{\pi}} \).

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

The maximum velocity and the maximum acceleration of a body executing simple harmonic oscillator are 2 m/s and 4 m/s2 and Then angular velocity will be A. 3 rad/sec B. 0.5 rad/sec C. 1 rad/sec D. 2 rad/sec

CBSE CLASS XII Related Questions

2.The resistance of a wire at 25°C is 10.0 \( \Omega \). When heated to 125°C, its resistance becomes 10.5 \( \Omega \). Find (i) the temperature coefficient of resistance of the wire, and (ii) the resistance of the wire at 425°C.

4.The electric field at a point in a region is given by \( \vec{E} = \alpha \frac{\hat{r}}{r^3} \), where \( \alpha \) is a constant and \( r \) is the distance of the point from the origin. The magnitude of potential of the point is:

5.Three batteries E1, E2, and E3 of emfs and internal resistances (4 V, 2 \(\Omega\)), (2 V, 4 \(\Omega\)) and (6 V, 2 \(\Omega\)) respectively are connected as shown in the figure. Find the values of the currents passing through batteries E1, E2, and E3.

6.A current carrying circular loop of area A produces a magnetic field \( B \) at its centre. Show that the magnetic moment of the loop is \( \frac{2BA}{\mu_0} \sqrt{\frac{A}{\pi}} \).

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

2.
The resistance of a wire at 25°C is 10.0 \( \Omega \). When heated to 125°C, its resistance becomes 10.5 \( \Omega \). Find (i) the temperature coefficient of resistance of the wire, and (ii) the resistance of the wire at 425°C.

4.
The electric field at a point in a region is given by \( \vec{E} = \alpha \frac{\hat{r}}{r^3} \), where \( \alpha \) is a constant and \( r \) is the distance of the point from the origin. The magnitude of potential of the point is:

5.
Three batteries E1, E2, and E3 of emfs and internal resistances (4 V, 2 \(\Omega\)), (2 V, 4 \(\Omega\)) and (6 V, 2 \(\Omega\)) respectively are connected as shown in the figure. Find the values of the currents passing through batteries E1, E2, and E3.

6.
A current carrying circular loop of area A produces a magnetic field \( B \) at its centre. Show that the magnetic moment of the loop is \( \frac{2BA}{\mu_0} \sqrt{\frac{A}{\pi}} \).