A particle of mass m is moving along the x-axis with initial velocity $$u\widehat i$$. It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If $$\sin {\theta _1} = \sqrt n \sin {\theta _2}$$ then value of n is ________.

A wire of density 9 $$ \times $$ 10^–3 kg cm^–3 is stretched between two clamps 1 m apart. The resulting strain in the wire is 4.9 $$ \times $$ 10^–4. The lowest frequency of the transverse vibrations in the wire is : (Young’s modulus of wire Y = 9 $$ \times $$ 10¹⁰ Nm^–2), (to the nearest integer), _________

A 10 $$\mu $$F capacitor is fully charged to a potential difference of 50 V. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes 20 V. The capacitance of the second capacitor is :

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is