A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first 2 sec, it rotates through an angle θ1. In the next 2 seconds, it rotates through an additional angle θ2. The ratio of θ2/θ1 is:
1. | 1 | 2. | 2 |
3. | 3 | 4. | 5 |
Two rotating bodies A and B of masses m and 2m with moments of inertia and have equal kinetic energy of rotation. If and be their angular momenta respectively, then:
1.
2.
3.
4.
A force F= is acting at a point r=--12. The value of α
for which angular momentum is conserved about the origin is:
1. -1
2. 2
3. zero
4. 1
The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:
1. B
2. C
3. D
4. A
Three masses are placed on the x-axis: \(300\) g at the origin, \(500\) g at \(x =40\) cm, and \(400\) g at \(x=70\) cm. The distance of the center of mass from the origin is:
1. | \(40\) cm | 2. | \(45\) cm |
3. | \(50\) cm | 4. | \(30\) cm |
Which of the following will not be affected if the radius of the sphere is increased while keeping mass constant?
1. | Moment of inertia | 2. | Angular momentum |
3. | Angular velocity | 4. | Rotational kinetic energy |
Four particles of mass m1 = 2m, m2 = 4m, m3 = m, and m4 are placed at the four corners of a square. What should be the value of so that the center of mass of all the four particles is exactly at the center of the square?
1. | 2m | 2. | 8m |
3. | 6m | 4. | None of these |
A rigid body rotates about a fixed axis with a variable angular velocity equal to \(\alpha\) \(-\) \(\beta t\), at the time t, where \(\alpha , \beta\) are constants. The angle through which it rotates before it stops is:
1. | \(\frac{\left(\alpha\right)^{2}}{2 \beta}\) | 2. | \(\frac{\left(\alpha\right)^{2} - \left(\beta\right)^{2}}{2 \alpha}\) |
3. | \(\frac{\left(\alpha\right)^{2} - \left(\beta\right)^{2}}{2 \beta}\) | 4. | \(\frac{\left(\alpha-\beta\right) \alpha}{2}\) |
The position of a particle is given by \(\vec r = \hat i+2\hat j-\hat k\) and momentum \(\vec P = (3 \hat i + 4\hat j - 2\hat k)\). The angular momentum is perpendicular to:
1. | X-axis |
2. | Y-axis |
3. | Z-axis |
4. | Line at equal angles to all the three axes |
The centre of the mass of 3 particles, 10 kg, 20 kg, and 30 kg, is at (0, 0, 0). Where should a particle with a mass of 40 kg be placed so that its combined centre of mass is (3, 3, 3)?
1. (0, 0, 0)
2. (7.5, 7.5, 7.5)
3. (1, 2, 3)
4. (4, 4, 4)