Consider a thin square plate floating on a viscous liquid in a large tank. The height $$h$$ of the liquid in the tank is much less than the width of the tank. The floating place is pulled horizontally with a constant velocity $${\mu _{0.}}$$ Which of the following statements is (are) true?

An infinitely long thin non-conducting wire is parallel to the $$z$$-axis and carries a uniform line charge density $$\lambda .$$ It pierces a thin non-conducting spherical shell of radius $$R$$ in such a way that the arc $$PQ$$ subtends an angle $${120^ \circ }$$ at the center $$O$$ of the spherical shell, as shown in the figure. The permittivity of free space is $${ \in _0}.$$ Which of the following statement is (are) true?

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $$100\,K$$ and the universal gas constant $$R=8.0$$ $$J\,mo{l^{ - 1}}{K^{ - 1}},$$ the decrease in its internal energy, in Joule, is ____________.

In a photoelectric experiment a parallel beam of monochromatic light with power of $$200$$ $$W$$ is incident on a perfectly absorbing cathode of work function $$6.25$$ $$ev.$$ The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is $$100\% $$. A potential difference of $$500$$ $$V$$ is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force $$F = n \times {10^{ - 4}}$$ $$N$$ due to the impact of the electrons. The value of $$n$$ is ______________. Mass of the electron $${M_e} = 9 \times {10^{ - 31}}\,kg$$ and $$1.0eV = 1.6 \times {10^{ - 19}}\,J.$$