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 \(\rho ( x) = a \left( 1 + bx^{2} \right)\) where, a, and b are constants and \(0 \leq x \leq 1\). The centre of mass of the rod will be at:
1. | \(\dfrac{3(2+b)}{4(3+b)}\) | 2. | \(\dfrac{4(2+b)}{3(3+b)}\) |
3. | \(\dfrac{3(3+b)}{4(2+b)}\) | 4. | \(\dfrac{4(3+b)}{3(2+b)}\) |
The centre of mass of an extended body on the surface of the earth and its centre of gravity:
(a) | are always at the same point for any size of the body. |
(b) | are always at the same point only for spherical bodies. |
(c) | can never be at the same point. |
(d) | is close to each other for objects, say of sizes less than 100 m. |
(e) | both can change if the object is taken deep inside the earth. |
Choose the correct alternatives:
1. (a, c)
2. (a, d)
3. (d) only
4. (c, d)