Three particles of masses \(100~\text{g}\), \(150~\text{g}\), and \(200~\text{g}\) respectively are placed at the vertices of an equilateral triangle of a side \(0.5~\text{m}\) long. What is the position of the centre of mass of three particles?

Position of centre of mass of a triangular lamina as shown in the figure is:

What is the position of centre of mass of a uniform L-shaped lamina (a thin flat plate) with dimensions as shown? The mass of the lamina is 3 kg.

If the force \(7\hat i+3\hat j-5\hat k\) acts on a particle whose position vector is \(\hat i - \hat j+\hat k\), the torque of the force about the origin is?
1. \(2\hat i +12\hat j+10\hat k\)
2. zero
3. \(2\hat i -12\hat j-10\hat k\)
4. \(2\hat i +12\hat j-10\hat k\)

The angular momentum about any point of a single particle moving with constant velocity:

Moment of a couple:

A metal bar 70 cm long and 4.00 kg in mass supported on two knife edges placed 10 cm from each end. A 6.00 kg load is suspended at 30 cm from one end as shown in the figure. The reactions ${\mathrm{R}}_1 \mathrm{and} {\mathrm{R}}_2$ at the knife-edges are: (Assume the bar to be of uniform cross-section and homogeneous.)

A \(3~\text{m}\) long ladder weighing \(20~\text{kg}\) leans on a frictionless wall. Its feet rest on the floor \(1~\text{m}\) from the wall as shown in the figure. The reaction forces of the wall and the floor respectively are:

The moment of inertia of a disc about one of its diameters is:

The moment of inertia of a rod of mass M, length l about an axis perpendicular to it through one end is:

1.  ${\mathrm{Ml}}^2$

2.  $\frac{{\mathrm{Ml}}^2}{2}$

3.  $\frac{{\mathrm{Ml}}^2}{3}$

4.  Can't be determined