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

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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

1.
An electron is revolving around a proton in a circular orbit of radius $r$. Using classical physics, prove that the ratio of value of the angular momentum and the value of magnetic moment of electron revolving in the orbit is a constant.

2.
Two point charges -Q and Q are located at points (d, 0) and (0, d) respectively, in x-y plane. The electric field E at the origin will be:

3.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

4.
A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is (i) $\sqrt{2}$, and (ii) $\sqrt{3}$.

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The number of free electrons per unit volume ($\text{m}^3$) in a wire made of copper (resistivity $1.72 \times 10^{-8}\,\Omega\,\text{m}$) is $8.5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.

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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

1.An electron is revolving around a proton in a circular orbit of radius $r$. Using classical physics, prove that the ratio of value of the angular momentum and the value of magnetic moment of electron revolving in the orbit is a constant.

2.Two point charges -Q and Q are located at points (d, 0) and (0, d) respectively, in x-y plane. The electric field E at the origin will be:

3.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

4.A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is (i) $\sqrt{2}$, and (ii) $\sqrt{3}$.

6.The number of free electrons per unit volume ($\text{m}^3$) in a wire made of copper (resistivity $1.72 \times 10^{-8}\,\Omega\,\text{m}$) is $8.5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
An electron is revolving around a proton in a circular orbit of radius $r$. Using classical physics, prove that the ratio of value of the angular momentum and the value of magnetic moment of electron revolving in the orbit is a constant.

2.
Two point charges -Q and Q are located at points (d, 0) and (0, d) respectively, in x-y plane. The electric field E at the origin will be:

3.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

4.
A ray of light MN is incident normally on the face corresponding with side AB of a prism with an isosceles right-angled triangular base ABC. Trace the path of the ray as it passes through the prism when the refractive index of the prism material is (i) $\sqrt{2}$, and (ii) $\sqrt{3}$.

6.
The number of free electrons per unit volume ($\text{m}^3$) in a wire made of copper (resistivity $1.72 \times 10^{-8}\,\Omega\,\text{m}$) is $8.5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.