Fig. shows the transverse circular section of a tunnel. At the highest point S, a 100 W lamp is lighted. The diameter of the tunnel is 4m. Compare the intensities of illumination at the lowest point P of the tunnel and at a point Q on the wall making an angle of depression of `60^(@)` at the bulb.

In Fig. the circular cross-section of tunnel is shown. A 100 W almp is lighted at the heighest point S. The diameter of the tunnel is 2m. Compare the illuminance at the lowest point P and the point Q of the tunnel.

A plane light wave with wavelength lambda = 0.57mu m falls normally on a suface on a surface of a glass (n = 1.60) disc which shuts one and a half Fresnel zones for the observation point P . What must the minimum thickness of that disc be for the intensity of light at the point P to be the highest ? Take into account the interference of light on its passing through the disc.

In a city, there is a circular park. There are four points of entry into the park, namely P, Q, R and S. Three paths were constructed which connected the points PQ, RS and PS. The length of the path PQ is 10 units and the length of the path RS is 7 units. Later, the municipal corporation extended the paths PQ and RS so that they meet at a point T on the main road outside the park. The path from Q to T measures 8 units and it was found that the angle PTS is 60^(@) . Find the area (in square units) enclosed by the paths PT, TS and PS

A bulb of 100 watt is hanging at a height of one meter above the centre of a circular table of diameter 4 m . If the intensity at a point on its rim is I_(0) , then the intensity at the centre of the table will be

The angle of elevation of the top of a vertical tower situated perpendicularly on a plane is observed as 60^(@) from a point P on the same plane .From another point Q , 10 m vertically above the point P , the angle of depression of the foot of the tower is 30^(@) The height of the tower is

A ball of mass m is moved with speed v_0 at the highest point in a closed circular tube of radius R kept in the vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.