Q. No.A meter scale is moving with uniform velocity. This implies:
1.
the force acting on the scale is zero, but a torque about the centre of mass can act on the scale.
2.
the force acting on the scale is zero and the torque acting about the centre of mass of the scale is also zero.
3.
the total force acting on it need not zero but the torque on it is zero.
4.
neither the force nor the torque needs to be zero.
The centre of mass of an extended body on the surface of the earth and its centre of gravity:
| (a) | are always at the same point for any size of the body. |
| (b) | are always at the same point only for spherical bodies. |
| (c) | can never be at the same point. |
| (d) | is close to each other for objects, say of sizes less than 100 m. |
| (e) | both can change if the object is taken deep inside the earth. |
Choose the correct alternatives:
2. (a), (d)
3. (d) only
4. (c), (d)
A uniform cube of mass \(m\) and side \(a\) is placed on a frictionless horizontal surface. A vertical force \(F\) is applied to the edge as shown in the figure. Match the following (most appropriate choice).
| List- I | List- II | ||
| (a) | \(mg/4<F<mg/2\) | (i) | cube will move up. |
| (b) | \(F>mg/2\) | (ii) | cube will not exhibit motion. |
| (c) | \(F>mg\) | (iii) | cube will begin to rotate and slip at \(A\). |
| (d) | \(F=mg/4\) | (iv) | normal reaction effectively at \(a/3\) from \(A\), no motion. |
| 1. | a - (i), b - (iv), c - (ii), d - (iii) |
| 2. | a - (ii), b - (iii), c - (i), d - (iv) |
| 3. | a - (iii), b - (i), c - (ii), d - (iv) |
| 4. | a - (i), b - (ii), c - (iv), d - (iii) |
With reference to the figure of a cube of edge \(a\) and mass \(m,\) the following statements are given. (\(O\) is the centre of the cube).
| (a) | The moment of inertia of the cube about the \(z\)-axis is \(I_z=I_x+I_y\) |
| (b) | The moment of inertia of the cube about the \(z'\)-axis is \({I_z}'=I_z+\frac{{ma}^2}{2}\) |
| (c) | The moment of inertia of the cube about \(z''\)-axis is = \(=I_z+\frac{{ma}^2}{2}\) |
| (d) | \(I_x=I_y\) |
| 1. | (a, c) | 2. | (a, d) |
| 3. | (b, d) | 4. | (b, c) |
The figure shows a lamina in \(xy\text{-}\)plane. Two axes \({z}\) and \(z'\) pass perpendicular to its plane. A force \(\vec{F}\) acts in the plane of the lamina at point \(P\) as shown in the figure.
(The point \(P\) is closer to the \(z'\text-\)axis than the \(z\text{-}\)axis.)
| (a) | torque \(\vec{\tau}\)caused by \(\vec{F}\)about \(z\text{-}\)axis is along \((-\hat{k})\) |
| (b) | torque \(\vec{\tau}'\)caused by \(\vec{F}\)about \(z'\text-\)axis is along \((-\hat{k})\) |
| (c) | torque caused by \(\vec{F}\)about the \(z\text{-}\)axis is greater in magnitude than that about the \(z'\text-\)axis |
| (d) | total torque is given by \(\vec{\tau}_{net}=\vec{\tau}+\vec{\tau}'\) |
Choose the correct option from the given ones:
| 1. | (c) and (d) only |
| 2. | (a) and (c) only |
| 3. | (b) and (c) only |
| 4. | (a) and (b) only |
The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?
| (a) | The forces may be acting radially from a point on the axis. |
| (b) | The forces may be acting on the axis of rotation. |
| (c) | The forces may be acting parallel to the axis of rotation. |
| (d) | The torque caused by some forces may be equal and opposite to that caused by other forces. |
Choose the correct option.
1. (a, c, d)
2. (a, b, d)
3. (a, b, c, d)
4. (b, c, d)
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 |
| (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) |
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. \(0\)
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. | \(\dfrac{4(3+b)}{3(2+b)}\) |
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