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

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 co–ordinate of the centre of mass of the five–plate system will be:

A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity $\omega$.  Four objects of mass m are held gently at the opposite ends of the ring's two perpendicular diameters. The angular velocity of the ring will be:

1. $\frac{\mathrm{M\omega }}{\mathrm{M}+ 4\mathrm{m}}$

2. $\frac{(\mathrm{M}+ 4\mathrm{m})\mathrm{\omega }}{\mathrm{M}}$

3. $\frac{(\mathrm{M}- 4\mathrm{m})\mathrm{\omega }}{\mathrm{M}+ 4\mathrm{m}}$

4. $\frac{\mathrm{M\omega }}{4\mathrm{m}}$

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

A rod of weight \(w\) is supported by two parallel knife edges, A and B, and is in equilibrium in a horizontal position. The knives are at a distance \(d\) from each other. The centre of mass of the rod is at a distance \(x \) from A. The normal reaction on A is:

Three-point masses each of mass 'm', are placed at the vertices of an equilateral triangle of side a. The moment of inertia of the system through a mass m at O and lying in the plane of COA and perpendicular to OA is:

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of $2$ $m{s}^{-1}.$ When the stone reaches the floor, the distance of the man above the floor will be: 

The moment of inertia of a uniform circular disc of radius 'R' and mass 'M' about an axis touching the disc at its diameter and normal to the disc will be:
1. $\frac{3}{2}M{R}^2$
2. $\frac{1}{2}M{R}^2$
3. $M{R}^2$
4. $\frac{2}{5}M{R}^2$

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:
 
1. B                   
2. C
3. D                   
4. A