A particle moves in the x-y plane according to rule and . The particle follows:
1. | an elliptical path. |
2. | a circular path. |
3. | a parabolic path. |
4. | a straight line path inclined equally to the x and y-axis. |
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The magnitude of a vector is constant but it is changing its direction continuously. The angle between and is:
1. 180°
2. 120°
3. 90°
4. 0°
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What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\) :
1. | \(6 \hat{i}+2 \hat{j}-3 \hat{k} \) |
2. | \(-18 \hat{i}-13 \hat{j}+2 \hat{k} \) |
3. | \(4 \hat{i}-13 \hat{j}+6 \hat{k}\) |
4. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
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The angle turned by a body undergoing circular motion depends on the time as given by the equation, . It can be deduced that the angular acceleration of the body is?
1. θ1
2. θ2
3. 2θ1
4. 2θ2
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A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:
1. | \(25\) m/s2 | 2. | \(36\) m/s2 |
3. | \(5\) m/s2 | 4. | \(15\) m/s2 |
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If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where θ is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is:
1. 8 rad/sec
2. 12 rad/sec
3. 24 rad/sec
4. 36 rad/sec
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A car moves on a circular path such that its speed is given by v = Kt, where K =constant and t is time. Also given: radius of the circular path is r. The net acceleration of the car at time t will be:
1.
2. 2K
3. K
4.
Two particles A and B are moving in a uniform circular motion in concentric circles of radii \(r_A\) and \(r_B\) with speeds \(v_A\) and \(v_B\) respectively. Their time periods of rotation are the same. The ratio of the angular speed of \(A\) to that of \(B\) will be:
1. | \( 1: 1 \) | 2. | \(r_A: r_B \) |
3. | \(v_A: v_B \) | 4. | \(r_B: r_A\) |
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A stone tied to the end of a 1 m long string is whirled in a horizontal circle at a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?
1. | \(\pi^2 \mathrm{~ms}^{-2} \) and direction along the tangent to the circle. |
2. | \(\pi^2 \mathrm{~ms}^{-2} \) and direction along the radius towards the centre. |
3. | \(\frac{\pi^2}{4} \mathrm{~ms}^{-2}\) and direction along the radius towards the centre. |
4. | \(\pi^2 \mathrm{~ms}^{-2} \) and direction along the radius away from the centre. |
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The position vector of a particle is . The velocity of the particle is:
1. | parallel to the position vector. |
2. | at 60° with position vector. |
3. | parallel to the acceleration vector. |
4. | perpendicular to the position vector. |
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