A body rotates about a fixed axis with an angular acceleration of 1 rad/sec2. Through what does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s?

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Ques: A body rotates about a fixed axis with an angular acceleration of 1 rad/sec2. Through what does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s?

Solution: In the given question, some known values are given as mentioned below:

Initial angular velocity of the fan, ω_i = 5 rad/s (Given)
Final angular velocity of the fan, ω_f = 15 rad/s (Given)
Angular acceleration, α = 1 rad/sec²(Given)

Here we will apply the equation of rotational motion for constant angular acceleration which is given as:

ω_f² = ω_i² + 2αθ

⇒ θ = \(\frac{\omega_f^2 - \omega_i^2}{2 \alpha}\)

Where

ω_f = final angular velocity
ω_i = initial angular velocity
α = angular acceleration
θ = angular displacement of the body during the time in which its angular velocity

Using the equation of rotational motion, angular displacement of the fan, is given by

θ = \(\frac{15^2-5^2}{2 \times 1}\) = \(\frac{225-25}{2}\) = 100 rad

Hence, the body rotates with an angular displacement of 100 rad during the time in which its angular velocity increases from 5 rad/s to 15 rad/s.

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A body rotates about a fixed axis with an angular acceleration of 1 rad/sec2. Through what does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s?

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A body rotates about a fixed axis with an angular acceleration of 1 rad/sec2. Through what does it rotate during the time in which its angular velocity increases from 5 rad/s to 15 rad/s?

CBSE CLASS XII Related Questions

1.Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

2.Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

3. Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

4.Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

5.Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

6. If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

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Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

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Write the expression for the magnetic field due to a current element in vector form. Consider a 1 cm segment of a wire, centered at the origin, carrying a current of 10 A in positive x-direction. Calculate the magnetic field \( \mathbf{B} \) at a point \( (1 \, \text{m}, 1 \, \text{m}, 0) \).

3.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

4.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

5.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

6.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.