For which of the following does the centre of mass lie outside the body?

1. A pencil             2. A shotput              3. A dice                4. A bangle

Which of the following points is the likely position of the center of mass of the system shown in the figure?

1. \(A\)
2. \(B\)
3. \(C\)
4. \(D\)

A uniform square plate has a small piece Q of an irregular shape removed and glued to the center of the plate leaving a hole behind in the figure. The CM of the plate is now in the following quadrant of the x-y plane. 

1. I

2. II

3. III

4. IV

The density of a non-uniform rod of length 1m is given by $\mathrm{\rho }\left(\mathrm{x}\right)=\mathrm{a}(1+{\mathrm{bx}}^2)$ where, a, and b are constants and $0\le x\le 1$. The centre of mass of the rod will be at

1. \(\frac{3(2+b)}{4(3+b)}\)
2. \(\frac{4(2+b)}{3(3+b)}\)
3. \(\frac{3(3+b)}{4(2+b)}\)
4. \(\frac{4(3+b)}{3(2+b)}\)

The centre of mass of an extended body on the surface of the earth and its centre of gravity:

Choose the correct alternatives:

1. (a, c)

2. (a, d)

3. (d) only

4. (c, d)