(a) | for a general rotational motion, angular momentum \(L\) and angular velocity \(\omega\) need not to be parallel. |
(b) | for a rotational motion about a fixed axis, angular momentum \(L\) and angular velocity \(\omega\) are always parallel. |
(c) | for a general translational motion, momentum \(p\) and velocity \(v\) are always parallel. |
(d) | for a general translational motion, acceleration \(a\) and velocity \(v\) are always parallel. |
1. | (a), (c) | 2. | (b), (c) |
3. | (c), (d) | 4. | (a), (b), (c) |
Which of the following points is the likely position of the center of mass of the system shown in the figure?
1. \(A\)
2. \(B\)
3. \(C\)
4. \(D\)
To maintain a rotor at a uniform angular speed of \(200\) rad s–1, an engine needs to transmit a torque of \(180\) N-m. What is the power required by the engine?
1. \(33\) kW
2. \(36\) kW
3. \(28\) kW
4. \(76\) kW
A non-uniform bar of weight \(W\) is suspended at rest by two strings of negligible weight as shown in the figure. The angles made by the strings with the vertical are \(36.9^\circ\) and \(53.1^\circ\) respectively. The bar is \(2\) m long. The distance \(d\) of the center of gravity of the bar from its left end is:
(Take sin\(36.9^\circ=0.6\) and sin\(53.1^\circ=0.8\))
1. \(69\) cm
2. \(72\) cm
3. \(79\) cm
4. \(65\) cm
In the \(\mathrm{HCl}\) molecule, the separation between the nuclei of the two atoms is about \(1.27~\mathring{\text A}~(1~\mathring{\text A}=10^{10}~\text m).\) Then the approximate location of the CM of the molecule is:
(Given that a chlorine atom is about \(35.5\) times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus).
1. | \(1.235~\mathring{\text A}\) from \(\mathrm{H-}\)atom |
2. | \(2.41~\mathring{\text A}\) from \(\mathrm{Cl-}\)atom |
3. | \(3.40~\mathring{\text A}\) from \(\mathrm{Cl-}\)atom |
4. | \(1.07~\mathring{\text A}\) from \(\mathrm{H-}\)atom |
For a body, with angular velocity \( \vec{\omega }=\hat{i}-2\hat{j}+3\hat{k}\) and radius vector \( \vec{r }=\hat{i}+\hat{j}++\hat{k},\) its velocity will be:
1. \(-5\hat{i}+2\hat{j}+3\hat{k}\)
2. \(-5\hat{i}+2\hat{j}-3\hat{k}\)
3. \(-5\hat{i}-2\hat{j}+3\hat{k}\)
4. \(-5\hat{i}-2\hat{j}-3\hat{k}\)
A rigid body rotates with an angular momentum of \(L.\) If its kinetic energy is halved, the angular momentum becomes:
1. \(L\)
2. \(L/2\)
3. \(2L\)
4. \(L/\)
A uniform rod of length \(200~ \text{cm}\) and mass \(500~ \text g\) is balanced on a wedge placed at \(40~ \text{cm}\) mark. A mass of \(2~\text{kg}\) is suspended from the rod at \(20~ \text{cm}\) and another unknown mass \(m\) is suspended from the rod at \(160~\text{cm}\) mark as shown in the figure. What would be the value of \(m\) such that the rod is in equilibrium? (Take \(g=10~( \text {m/s}^2)\)
1. | \({\dfrac 1 6}~\text{kg}\) | 2. | \({\dfrac 1 {12}}~ \text{kg}\) |
3. | \({\dfrac 1 2}~ \text{kg}\) | 4. | \({\dfrac 1 3}~ \text{kg}\) |
Five particles of mass \(2\) kg each are attached to the circumference of a circular disc of a radius of \(0.1\) m and negligible mass. The moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane will be:
1. \(1\) kg-m2
2. \(0.1\) kg-m2
3. \(2\) kg-m2
4. \(0.2\) kg-m2