A small spherical droplet of density d is floating exactly half immersed in a liquid of density $$\rho $$ and surface tension T. The radius of the droplet is (take note that the surface tension applies an upward force on the droplet) :

In LC circuit the inductance L = 40 mH and
capacitance C = 100 $$\mu $$F. If a voltage
V(t) = 10sin(314t) is applied to the circuit, the
current in the circuit is given as :

A plane electromagnetic wave is propagating along the direction $${{\widehat i + \widehat j} \over {\sqrt 2 }}$$ , with its polarization along the direction $$\widehat k$$ . The correct form of the magnetic field of the wave would be (here B₀ is an appropriate constant) :

A rod of length L has non-uniform linear mass
density given by $$\rho $$(x) = $$a + b{\left( {{x \over L}} \right)^2}$$ , where a
and b are constants and 0 $$ \le $$ x $$ \le $$ L. The value
of x for the centre of mass of the rod is at :