A wire of density $$8 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$$ is stretched between two clamps $$0.5 \mathrm{~m}$$ apart. The extension developed in the wire is $$3.2 \times 10^{-4} \mathrm{~m}$$. If $$Y=8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$$, the fundamental frequency of vibration in the wire will be ___________ $$\mathrm{Hz}$$.

A metallic cube of side $$15 \mathrm{~cm}$$ moving along $$y$$-axis at a uniform velocity of $$2 \mathrm{~ms}^{-1}$$. In a region of uniform magnetic field of magnitude $$0.5 \mathrm{~T}$$ directed along $$z$$-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be _________ mV.

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $$1: 2^{1 / 3}$$. Their respective speed have a ratio of $$n: 1$$. The value of $n$ is __________.

A block of mass $$5 \mathrm{~kg}$$ starting from rest pulled up on a smooth incline plane making an angle of $$30^{\circ}$$ with horizontal with an affective acceleration of $$1 \mathrm{~ms}^{-2}$$. The power delivered by the pulling force at $$t=10 \mathrm{~s}$$ from the start is ___________ W.

[use $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ ]

(calculate the nearest integer value)