Let \(\omega_{1},\omega_{2}\) and \(\omega_{3}\) be the angular speed of the second hand, minute hand, and hour hand of a smoothly running analog clock, respectively. If \(x_{1},x_{2}\) and \(x_{3}\) are their respective angular distance in \(1\) minute then the factor which remains constant \((k)\) is:
1. \(\frac{\omega_1}{x_1}\text=\frac{\omega_2}{x_2}\text=\frac{\omega_3}{x_3}\text={k}\)
2. \(\omega_{1}x_{1}\text=\omega_{2}x_{2}\text=\omega_{3}x_{3}\text={k}\)
3. \(\omega_{1}x_{1}^{2}\text=\omega_{2}x_{2}^{2}\text=\omega_{3}x_{3}^{2}\text={k}\)
4. \(\omega_{1}^{2}x_{1}\text=\omega_{2}^{2}x_{2}\text=\omega_{3}^{2}x_{3}\text={k}\)
Subtopic:  Rotational Motion: Kinematics |
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The angular acceleration of a body, moving along the circumference of a circle, is:
1. along the axis of rotation
2. along the radius, away from centre
3. along the radius towards the centre
4. along the tangent to its position
Subtopic:  Rotational Motion: Kinematics |
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A constant torque of \(100\) N-m turns a wheel of moment of inertia \(300\) kg-m2 about an axis passing through its centre. Starting from rest, its angular velocity after \(3\) s is: 
1. \(1\) rad/s 
2. \(5\) rad/s
3. \(10\) rad/s
4. \(15\) rad/s
Subtopic:  Rotational Motion: Kinematics |
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The angular speed of a flywheel moving with uniform angular acceleration changes from \(1200\) rpm to \(3120\) rpm in \(16\) s. The angular acceleration in rad/s² is:
1. \(104 \pi\)
2. \(2\pi\)
3. \(4\pi\)
4. \(12\pi\)
Subtopic:  Rotational Motion: Kinematics |
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The angular speed of the wheel of a vehicle is increased from \(360~\text{rpm}\) to \(1200~\text{rpm}\) in \(14\) seconds. Its angular acceleration will be:
1. \(2\pi ~\text{rad/s}^2\)
2. \(28\pi ~\text{rad/s}^2\)
3. \(120\pi ~\text{rad/s}^2\)
4. \(1 ~\text{rad/s}^2\)

Subtopic:  Rotational Motion: Kinematics |
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A particle starting from rest moves in a circle of radius \(r\). It attains a velocity of \(v_0~\text{m/s}\) on completion of \(n\) rounds. Its angular acceleration will be:
1. \( \dfrac{v_0}{n} ~\text{rad} / \text{s}^2\)
2. \( \dfrac{v_0^2}{2 \pi {nr}^2}~ \text{rad} / \text{s}^2 \)
3. \( \dfrac{v_0^2}{4 \pi {n}{r}^2}~ \text{rad} / \text{s}^2 \)
4. \( \dfrac{v_0^2}{4 \pi {nr}} ~\text{rad} / \text{s}^2 \)

Subtopic:  Rotational Motion: Kinematics |
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