When a stick is released (as shown in the figure below), its free end velocity when it strikes the ground is:

1. 4.2 m/s
2. 1.4 m/s
3. 2.8 m/s
4. $\sqrt{6}$ m/s

If a rod of length 3 m with its mass acting per unit length, is directly proportional to distance x from one of its ends, then its centre of gravity from that end will be at: 

Consider a system of two particles having masses m₁ and m₂. If the particle of mass m₁ is pushed towards the mass centre of particles through a distance 'd', by what distance would the particle of mass m₂ move so as to keep the mass centre of particles at the original position ?

1. $\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}\mathrm{d}$

2. d

3. $\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}$

4. $\frac{{\mathrm{m}}_1}{{\mathrm{m}}_1+{\mathrm{m}}_2}\mathrm{d}$