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 \(\vec{F}=\alpha\hat i+3\hat j+6\hat k\) is acting at a point \(\vec{r}=2\hat i-6\hat j-12\hat k.\) The value of \(\alpha\)
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 \(m_1 = 2m\), \(m_2=4m\), \(m_3 =m \), and \(m_4\) are placed at the four corners of a square. What should be the value of \(m_4\) so that the centre of mass of all the four particles is exactly at the centre 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. | \(\frac{\alpha^{2}}{2 \beta}\) | 2. | \(\frac{\alpha^{2} -\beta^{2}}{2 \alpha}\) |
3. | \(\frac{\alpha^{2} - \beta^{2}}{2 \beta}\) | 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. \((4,4,4)\)