Particle A of mass m₁ moving with velocity $$\left( {\sqrt3\widehat i + \widehat j} \right)m{s^{ - 1}}$$ collides with another particle B of mass m₂ which is at rest initially. Let $$\overrightarrow {{V_1}} $$ and $$\overrightarrow {{V_2}} $$ be the velocities of particles A and B after collision respectively. If m₁ = 2m₂ and after
collision $$\overrightarrow {{V_1}} = $$$$\left( {\widehat i + \sqrt 3 \widehat j} \right)$$ , the angle between $$\overrightarrow {{V_1}} $$ and $$\overrightarrow {{V_2}} $$ is :

A particle moving in the xy plane experiences a velocity dependent force
$$\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)$$ , where v_x and v_y are the
x and y components of its velocity $$\overrightarrow v $$ . If $$\overrightarrow a $$ is the
acceleration of the particle, then
which of the following statements is true for the particle?

In a series LR circuit, power of 400W is dissipated from a source of 250 V, 50 Hz. The power factor of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as $$\left( {{n \over {3\pi }}} \right)$$ $$\mu $$F, then value of n is __________.

The centre of mass of solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then value of x is __________.