A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 $$ \times $$ 10^-2 m. The magnetic field at the center of the triangle will be :

A thin uniform bar of length $$L$$ and mass $$8$$ m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2$$\upsilon $$ and $$\upsilon $$ respectively. The masses stick to the bar after collision at a distance $${L \over 3}$$ and $${L \over 6}$$ respectively from the center of the bar. If the br starts rotating about its center of mass as a result of collision, the angular speed of the bar will be :

A parallel plate capacitor with area 200 cm² and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is $$25 \times {10^{ - 6}}N,$$ the value of V is approximately : $$\left( {{ \in _o} = 8.85 \times {{10}^{ - 12}}{{{C^2}} \over {N.{m^2}}}} \right)$$

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms^-1 is :
[k_B =1.4 $$ \times $$ 10^-23 J/K; m_He = 7 $$ \times $$ 10 ^-27 kg ]