An automobile engine develops 100 kW when rotating at a speed of 1800 rev/min. What torque does it deliver ?

1. 350 N-m

2. 440 N-m

3. 531 N-m

4. 628 N-m

In an orbital motion, the angular momentum vector is 

1. Along the radius vector

2. Parallel to the linear momentum

3. In the orbital plane

4. Perpendicular to the orbital plane

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. \(F(\hat i - \hat j)\)

A wheel whose moment of inertia is 12 ${\mathrm{Kgm}}^2$ has an initial angular velocity of 40 rad/sec. A constant torque of 20 Nm acts on the wheel. The time in which the wheel is accelerated to 100 rad/sec is

1.  72 seconds

2.  16 seconds

3.  8 seconds

4.  36 seconds

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. \(12A_0\)

A solid cylinder rolls down an inclined plane that has friction sufficient to prevent sliding. The ratio of rotational energy to total kinetic energy is

1.  $\frac{1}{2}$

2.  $\frac{1}{3}$

3.  $\frac{2}{3}$

4.  $\frac{3}{4}$

A swimmer while jumping into water from a height easily forms a loop in the air, if

Assertion : A ladder is more apt to slip when you are high up on it than when you just begin to climb

Reason : At the high point on a ladder, the torque is large and on climbing up the torque is small

Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

1.  5 I

2.  3 I

3.  6 I

4.  4 I