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

1.  $\left(\frac{5}{18}, \frac{1}{3\sqrt{3}}\right)$

2.  $\left(\frac{1}{4}, 0\right)$

3.  $\left(0, \frac{1}{4}\right)$

4.  $\left(\frac{1}{3\sqrt{3}}, \frac{5}{18}\right)$

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.

1.  $\left(\frac{6}{5}, \frac{6}{5}\right)$

2.  $\left(\frac{1}{5}, \frac{6}{5}\right)$

3.  $\left(\frac{5}{6}, \frac{5}{6}\right)$

4.  Can't be determined

If the force $7\hat{\mathrm{i}}+3\hat{\mathrm{j}}-5\hat{\mathrm{k}}$ acts on a particle whose position vector is $\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$, the torque of the force about the origin is?

1.  $2\hat{\mathrm{i}}+12\hat{\mathrm{j}}+10\hat{\mathrm{k}}$

2.  0

3.  $2\hat{\mathrm{i}}-12\hat{\mathrm{j}}-10\hat{\mathrm{k}}$

4.  $2\hat{\mathrm{i}}+12\hat{\mathrm{j}}-10\hat{\mathrm{k}}$

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

1.  increases continuously.

2.  decreases continuously.

3.  first increases then decrease.

4.  remains constant throughout the motion.

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.)

1.  43.12 N and 54.88 N

2.  54.88 N and 4.312 N

3.  54.88 N and 43.12 N

4.  43.12 N and 5.488 N

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

1.  30.4 N and 198 N

2.  199 N and 30 N

3.  30 N and 199 N

4.  34.6 N and 199 N

 The moment of inertia of a disc about one of its diameters is: 
1. ${\mathrm{MR}}^2$
2. $\frac{{\mathrm{MR}}^2}{3}$
3. $\frac{2{\mathrm{MR}}^2}{3}$
4. $\frac{{\mathrm{MR}}^2}{4}$

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