A boat of length \(10\) m and a mass of \(450\) kg is floating without motion in still water. A man of \(50\) kg standing at one end walks to the other end and comes to a stop. The magnitude of the displacement of the boat relative to the ground is:

1.	zero	2.	\(1\) m
3.	\(2\) m	4.	\(5\) m

A uniform rod of mass 2M is bent into four adjacent semicircles, each of radius r, all lying in the same plane. The moment of inertia of the bent rod about an axis through one end A and perpendicular to the plane of the rod is:
      

1. 22 ${\mathrm{Mr}}^2$

2. 88 ${\mathrm{Mr}}^2$

3. 44 ${\mathrm{Mr}}^2$

4. 66 ${\mathrm{Mr}}^2$

A hollow cylinder with an inner radius of R, an outer radius of 2R, and a mass M is rolling without slipping at the speed of its centre v. Its kinetic energy will be:
  

1. $\frac{11}{16}M{v}^2$

2. $\frac{7}{4}M{v}^2$

3. $\frac{13}{16}M{v}^2$

4. None of these

Five uniform circular plates, each of diameter \(D\) and mass \(m\), are laid out as shown in the figure. Using the origin shown, the \(y\text-\text{coordinate}\) of the centre of mass of the ''five–plate'' system will be:

A wheel of radius R rolls without slipping on the ground with a uniform velocity v. The relative acceleration of the topmost point of the wheel with respect to the bottommost point is:

1. $\frac{{\mathrm{v}}^2}{\mathrm{R}}$

2. $\frac{2{\mathrm{v}}^2}{\mathrm{R}}$

3. $\frac{{\mathrm{v}}^2}{2\mathrm{R}}$

4. $\frac{4{\mathrm{v}}^2}{\mathrm{R}}$

A horizontal heavy uniform bar of weight \(W\) is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to:

A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m are attached gently to the opposite ends of the diameter of the ring, the ring will then rotate with an angular velocity:

A solid cylinder of mass \(50\) kg and radius \(0.5\) m is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other end hanging freely. The tension in the string required to produce an angular acceleration of \(2\) revolutions/s² will be:
1. \(25\) N
2. \(50\) N
3. \(78.5\) N
4. \(157\) N