The value of M, as shown, for which the rod will be in equilibrium is (rod is massless)

1.  1 kg

2.  2 kg

3.  4 kg

4.  6 kg

The minimum coefficient of friction for a solid sphere to roll without slipping on an inclined plane of inclination 45$°$ is

1.  2/7

2.  1/3

3.  1/2

4.  2/5

A wheel is rolling along a horizontal ground with a speed o 10 m/s. The magnitude of the velocity of the points at the extremities of the horizontal diameter of the wheel is equal to

(1) $2\sqrt{10} m/s$

(2) 10 m/s

(3) $\sqrt{10} m/s$

(4) $10\sqrt{2} m/s$

$\mathrm{A} \mathrm{body} \mathrm{of} \mathrm{mass} \mathrm{m} \mathrm{is} \mathrm{projected} \mathrm{at} \mathrm{a} \mathrm{velocity} {\mathrm{v}}_0$
$\mathrm{with} \mathrm{an} \mathrm{angle} \mathrm{of} \mathrm{projection} \mathrm{\theta }. \mathrm{Angular} \mathrm{momentum}$
$\mathrm{L} \mathrm{of} \mathrm{body} \mathrm{after} \mathrm{time} \mathrm{t} \mathrm{w}.\mathrm{r}.\mathrm{to} \mathrm{origin} \mathrm{is} \mathrm{proportional} \mathrm{to}:$
$1. \mathrm{L}\propto \mathrm{t} 2. \mathrm{L}\propto {\mathrm{t}}^2$
$3. \mathrm{L}\propto {\mathrm{t}}^0 4. \mathrm{L}\propto \sqrt{\mathrm{t}}$

A mass M is moving with constant velocity parallel to the X-axis. Its angular momentum with respect to origin is:

1.  Zero

2.  Remains constant

3.  goes on increasing

4.  goes on decreasing

If I is the moment of inertia of a solid sphere about an axis parallel to diameter of a shpere and at a distance x from it. Which of the following graph represents the variation of I with X?

A particle is rotating under the central force, in which one of the following quantities is constant:

1.  torque

2.  angular momentum

3.  linear momentum

4.  none of these

A small object of uniform density rolls up a curved surface with an initial velocity \(v.\) It is reached upto a maximum height of \(\frac{3v^{2}}{4g}\) with respect to the initial position. The object is:

1. ring
2. solid sphere
3. hollow sphere
4. disc

A point is at (x, y, z). What is its moment of inertia about x-axis:

1.  $\mathrm{m}\left({\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2\right)$

2.  $\mathrm{m}\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)$

3.  $\mathrm{m}\left({\mathrm{y}}^2+{\mathrm{z}}^2\right)$

4.  $\mathrm{m}\left({\mathrm{x}}^2+{\mathrm{z}}^2\right)$

The disc is placed on the rough horizontal surface given only angular velocity ${\omega }_0$. The velocity of the centre of mass when it starts pure rolling is:

1.  $\frac{{\omega }_{0}R}{2}$

2.  $\frac{{\omega }_{0}R}{3}$

3.  $\frac{{\omega }_{0}R}{4}$

4.  $\frac{{\omega }_{0}R}{6}$