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?

CBSE CLASS XII Related Questions

1.
A current of \(4.0\,\text{A}\) flows through a wire of length \(1\,\text{m}\) and cross-sectional area \(1.0\,\text{mm}^2\), when a potential difference of \(2\,\text{V}\) is applied across its ends. Calculate the resistivity of the material of the wire.

3.
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:

5.
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?

6.
In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is

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Comments

dOGVmW

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.A current of \(4.0\,\text{A}\) flows through a wire of length \(1\,\text{m}\) and cross-sectional area \(1.0\,\text{mm}^2\), when a potential difference of \(2\,\text{V}\) is applied across its ends. Calculate the resistivity of the material of the wire.

3.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:

5.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?

6.In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is

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Comments

dOGVmW

1.
A current of \(4.0\,\text{A}\) flows through a wire of length \(1\,\text{m}\) and cross-sectional area \(1.0\,\text{mm}^2\), when a potential difference of \(2\,\text{V}\) is applied across its ends. Calculate the resistivity of the material of the wire.

3.
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:

5.
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?

6.
In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is