Question:
A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ is :
A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ is :
Updated On: Apr 12, 2026
- 6
- 3
- 4
- $1/3$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
For uniform angular acceleration, we use the equation $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$. Since it starts from rest, $\omega_0 = 0$.
Step 2: Detailed Explanation:
Let angular acceleration be $\alpha$.
In first 2 s: $\theta_1 = \frac{1}{2} \alpha (2)^2 = 2\alpha$.
Total angle in first 4 s: $\theta_{total} = \frac{1}{2} \alpha (4)^2 = 8\alpha$.
Angle in the next 2 s (from $t=2$ to $t=4$): $\theta_2 = \theta_{total} - \theta_1 = 8\alpha - 2\alpha = 6\alpha$.
Ratio $\frac{\theta_2}{\theta_1} = \frac{6\alpha}{2\alpha} = 3$.
Step 3: Final Answer:
The ratio is 3.
For uniform angular acceleration, we use the equation $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$. Since it starts from rest, $\omega_0 = 0$.
Step 2: Detailed Explanation:
Let angular acceleration be $\alpha$.
In first 2 s: $\theta_1 = \frac{1}{2} \alpha (2)^2 = 2\alpha$.
Total angle in first 4 s: $\theta_{total} = \frac{1}{2} \alpha (4)^2 = 8\alpha$.
Angle in the next 2 s (from $t=2$ to $t=4$): $\theta_2 = \theta_{total} - \theta_1 = 8\alpha - 2\alpha = 6\alpha$.
Ratio $\frac{\theta_2}{\theta_1} = \frac{6\alpha}{2\alpha} = 3$.
Step 3: Final Answer:
The ratio is 3.
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
View More Questions
Top JEE Main Rotational Mechanics Questions
- Two discs have the same moment of inertia about their axis. Their thicknesses are \(t_1\) and \(t_2\) and they have the same density. If \( \dfrac{R_1}{R_2} = \dfrac{1}{2} \), find \( \dfrac{t_1}{t_2} \).
- Find the moment of inertia about the given axis. Two solid spheres are arranged as shown. Given: \[ m_1 = 10\,\text{kg},\; R_1 = 20\,\text{cm}; \qquad m_2 = 5\,\text{kg},\; R_2 = 10\,\text{cm} \]
- Two discs have the same moment of inertia about their axes. Their thicknesses are \(t_1\) and \(t_2\) and they have the same density. If \( \dfrac{R_1}{R_2} = \dfrac{1}{2} \), then find \( \dfrac{t_1}{t_2} \).
A thin uniform rod (\(X\)) of mass \(M\) and length \(L\) is pivoted at a height \( \left(\dfrac{L}{3}\right) \) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top is ________. (\(g\) = gravitational acceleration)
- A uniform solid cylinder of length \(L\) and radius \(R\) has moment of inertia about its axis equal to \(I_1\). A small co-centric cylinder of length \(L/2\) and radius \(R/3\) carved from it has moment of inertia about its axis equal to \(I_2\). The ratio \(I_1/I_2\) is ________.
View More Questions
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
View More Questions