A wheel of radius R rolls on the ground with a uniform velocity v. The velocity of topmost point relative to the bottommost point is

1. v

2. 2v

3. v/2

4. zero

 

If the net external forces acting on the system of particles is zero, then which of the following may vary ?

1. Momentum of the system

2. Velocity of centre of mass

3. Position of centre of mass

4. None of the above

A wheel is rotating about an axis through its centre at \(720~\text{rpm}.\) It is acted upon by a constant torque opposing its motion for \(8\) seconds to bring it to rest finally. The value of torque in \((\text{N-m })\) is:
(given \(I=\frac{24}{\pi}~\text{kg.m}^2)\) 
1. \(48\)
2. \(72\)
3. \(96\)
4. \(120\)

A wheel is rotating 900 rpm about its axis. When power is cut off it comes to rest in 1 min. The angular retardation in rad/s² is 

1. $\mathrm{\pi }/2$

2. $\mathrm{\pi }/4$

3. $\mathrm{\pi }/6$

4. $\mathrm{\pi }/8$

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. \(12A_0\)