A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision,

A series RC-current is connected to AC voltage source. Consider two cases : (A) When C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current I_{R} through the resistor and voltage V_{C} across the capacitor are compared in the two cases. Which of the following is/are true?

A series RC combination is connected to an AC voltage of angular frequency $$\omega$$ = 500 rad/s. If the impedance of the RC circuit is R$$\sqrt{1.25}$$, the time constant (in millisecond) of the circuit is __________.

A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the spheres is A $$\times$$ 10^{2} (where 1 < A < 10). The value of Z is _____________.