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 $R_1~\text{and}~R_2$ at the knife-edges are: (Assume the bar to be of uniform cross-section and homogeneous.)

1. $43.12~\text{N}~\text{and}~54.88~\text{N}$
2. $54.88~\text{N}~\text{and}~4.312~\text{N}$
3. $54.88~\text{N}~\text{and}~43.12~\text{N}$
4. $43.12~\text{N}~\text{and}~5.488~\text{N}$

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