A uniform wooden stick of mass 1.6 kg and length $$l$$ rests in an inclined manner on a smooth, vertical wall of height h ( < $$l$$ ) such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $$30^\circ $$ with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio $${h \over l}$$ and the frictional force f at the bottom of the stick are ( g =10 ms^-2 )

A parallel beam of light is incident from air at an anglea on the side PQ of a right angled triangular prism of refractive index n = $$\sqrt 2 $$. Light undergoes total internal reflection in the prism at the face PR when a has a minimum value of 45°. The angle q of the prism is :

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength ($$\lambda $$) of incident light and the corresponding stopping potential (V₀) are given below:

$$\lambda \left( {\mu m} \right)$$	V0(Volt)
0.3	2.0
0.4	1.0
0.5	0.4

Given that c = 3 $$ \times $$ 10⁸ ms^-1 and e = 1.6 $$ \times $$ 10^-19 C, Planck's constant (in units of J-s) found from such an experiment is) :

A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load).
The temperature of water fed into the device cannot exceed 30°C and the entire stored 120 litres of water is initially cooled to 10°C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is :

(Specific heat of water is 4.2 kJ kg⁻¹ K⁻¹ and the density of water is 1000 kg m⁻³)