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. | \(6 \hat{i}-2 \hat{j}+8 \hat{k}\) |
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
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.
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. |
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. |
A car is moving at a speed of 40 m/s on a circular track of radius 400 m. This speed is increasing at the rate of 3 m/s2. The acceleration of the car is:
1. 4 m/s2
2. 7 m/s2
3. 5 m/s2
4. 3 m/s2
Certain neutron stars are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be:
1. | \(20 \times 10^8 \mathrm{~m} / \mathrm{s}^2 \) | 2. | \(8 \times 10^5 \mathrm{~m} / \mathrm{s}^2 \) |
3. | \(120 \times 10^5 \mathrm{~m} / \mathrm{s}^2 \) | 4. | \(4 \times 10^8 \mathrm{~m} / \mathrm{s}^2\) |
A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is:
1.
2.
3.
4.