The acceleration due to gravity on the earth’s surface at the poles is g and angular velocity of the earth about the axis passing through the pole is $$\omega $$. An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is (h << R, where R is the radius of the earth)

A ring is hung on a nail. It can oscillate, without slipping or sliding
(i) in its plane with a time period T₁ and,
(ii) back and forth in a direction perpendicular to its plane,
with a period T₂. The ratio $${{{T_1}} \over {{T_2}}}$$ will be :

The surface of a metal is illuminated alternately with photons of energies E₁ = 4 eV and E₂ = 2.5 eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is _____.

Two coherent sources of sound, S₁ and S₂, produce sound waves of the same wavelength, $$\lambda $$ = 1 m, in phase. S₁ and S₂ are placed 1.5 m apart (see fig). A listener, located at L, directly in front of S₂ finds that the intensity is at a minimum
when he is 2 m away from S₂. The listener moves away from S₁, keeping his distance from S₂ fixed. The adjacent maximum of intensity is observed when the listener is at a distance d from S₁. Then, d is :