Q. No.For which of the following does the centre of mass lie outside the body?
1. A pencil
2. A shotput
3. A dice
4. A bangle
1. A pencil
2. A shotput
3. A dice
4. A bangle
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. \(D\)
A particle of mass \(m\) is moving in \(yz\text-\)plane with a uniform velocity \(v\) with its trajectory running parallel to the \(+\text{ve}\) \(y\text{-}\)axis and intersecting \(z\text{-}\)axis at \(z=a\) in the figure. The change in its angular momentum about the origin as it bounces elastically from a wall at \(y\) = constant is:
| 1. | \(mva~\hat e_{x}\) | 2. | \(2mva~\hat e_{x}\) |
| 3. | \(ymva~\hat e_{x}\) | 4. | \(2ymva~\hat e_{x}\) |
When a disc rotates with uniform angular velocity, which of the following is not true?
| 1. | the sense of rotation remains the same. |
| 2. | the orientation of the axis of rotation remains the same. |
| 3. | the speed of rotation is non-zero and remains the same. |
| 4. | the angular acceleration is non-zero and remains the same. |
A uniform square plate has a small piece \(Q\) of an irregular shape removed and glued to the center of the plate leaving a hole behind in the figure. Then the moment of inertia about the \({z}\text -\)axis is:
| 1. | increased |
| 2. | decreased |
| 3. | the same |
| 4. | changed in an unpredictable manner |
A uniform square plate has a small piece \(Q\) of an irregular shape removed and glued to the center of the plate leaving a hole behind in the figure. The \(COM\) of the plate is now in the following quadrant of the \(x\text-y\) plane.
1. \(\text{I}\)
2. \(\text{II}\)
3. \(\text{III}\)
4. \(\text{IV}\)
The density of a non-uniform rod of length 1m is given by \(\rho ( x) = a \left( 1 + bx^{2} \right)\) where, \(a\), and \(b\) are constants and \(0 \leq x \leq 1\). The centre of mass of the rod will be at:
| 1. | \(\dfrac{3(2+b)}{4(3+b)}\) | 2. | \(\dfrac{4(2+b)}{3(3+b)}\) |
| 3. | \(\dfrac{3(3+b)}{4(2+b)}\) | 4. | \(\dfrac{4(3+b)}{3(2+b)}\) |
A merry-go-round, made of a ring-like platform of radius \(R\) and mass \(M,\) is revolving with the angular speed . A person of mass \(M\) is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round afterwards is:
1. \(\omega\)
2. \(2\omega\)
3. \(\omega/2\)
4. \(0\)
| (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. |
Choose the correct option from the given ones:
| 1. | (a) and (c) | 2. | (b) and (c) |
| 3. | (c) and (d) | 4. | (a), (b) and (c) |
Consider the following statements.
| (a) | angular momentum \(l_1\) of particle \(1\) about \(A\) is \(l_1=mv(d_1)\) ⊙ |
| (b) | angular momentum \(l_1\) of particle \(2\) about \(A\) is \(l_1=mv(r_2)\) ⊙ |
| (c) | total angular momentum of the system about \(A\) is \(l=mv(r_1+r_2)\) ⊙ |
| (d) | total angular momentum of the system about \(A\) is \(l=mv(d_2-d_1)\) ⊗ |
Choose the correct option from the given ones:
| 1. | (a), (c) only |
| 2. | (a), (d) only |
| 3. | (b), (d) only |
| 4. | (b), (c) only |
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