A wheel is at rest. Its angular velocity increases uniformly and becomes 80 rad/s after 5 s. The total angular displacement is 

1. 800 rad

2. 400 rad

3. 200 rad

4. 100 rad

A force$- F \hat k$ acts on $O$, the origin of the coordinate system. The torque at the point $(1,-1)$ will be:
1. $-F(\hat i + \hat j)$
2. $F(\hat i + \hat j)$
3. $-F(\hat i -\hat j)$
4. $F(\hat i - \hat j)$

Moment of inertia of an object does not depend upon

A thin uniform circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with an angular velocity $\omega$. Another disc of the same dimensions but of mass $\frac{1}{4}M$ is placed gently on the first disc co-axially. The angular velocity of the system will be:

When a torque acting upon a system is zero, then which of the following will be constant 

A flywheel is in the form of a uniform circular disc of radius 1 m and mass 2 kg. The work which must be done on it to increase its frequency of rotation from 5 rev ${\mathrm{s}}^{-1}$ to 10 rev ${\mathrm{s}}^{-1}$ is approximately

1.  1.5 x ${10}^2$ J

2.  3.0 x ${10}^2$ J

3.  1.5 x ${10}^3$ J

4.  3.0 x ${10}^3$ J

A constant torque acting on a uniform circular wheel changes its angular momentum from $A_0$ to $4A_0$ in $4~\text{s}$. The magnitude of this torque is:
1. $\dfrac{3A_0}{4}$
2. $4A_0$
3. $A_0$
4. $12A_0$

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D${}_1$ has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s${}^{-1}$. Disc D${}_2$ has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s${}^{-1}$. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad.s${}^{-1}$) of the system is

1. 60

2. 100

3. 120

4. 40