(i) Explain the use of screw gauge and vernier caliper in measuring smaller distances.
(ii) Write a note on triangultion method and radar method to measure larger distances.

Explanation

(i) Measurement of small distances: screw gauge and vernier caliper Screw gauge:
The screw gauge is an instrument used for measuring accurately the dimensions of objects up to a maximum of about 50 mm. The principle of the instrument is the magnification of linear motion using the circular motion of a screw. The least count of the screw gauge is 0.01 mm
Vernier caliper: A vernier caliper is a versatile instrument for measuring the dimensions of an object namely diameter of a hole, or a depth of a hole. The least count of the vernier caliper is 0.1 mm.

(ii) Triangulation method for the height of an accessible object:
Let AB = h be the height of the tree or tower to be measured. Let C be the point of observation at distance x from B. Place a range finder at C and measure the angle of elevation, ACB = `theta` as shown in figure.
From right angled triangle ABC,
tan `theta = (AB)/(BC) = h/x` (or) height h = x tan `theta`
Knowing the distance x, the height h can be determined

RADAR method
The word RADAR stands for radio detection and ranging. A radar can be used to measure accurately the distance of a nearby planet such as Mars. In this method, radio waves are sent from transmitters which, after reflection from the planet, are detected by the receiver. By measuring, the time interval (t) between the instants the radio waves are sent and received, the distance of the planet can be determined as where v is the speed of the radio wave. As the time taken (t) is for the distance covered during the forward and backward path of the radio waves, it is divided by 2 to get the actual distance of the object. This method can also be used to determine the height, at which an aeroplane flies from the ground.
`d = (x xx t)/(2)`
Speed = distance travelled `//` time taken
Distance(d) = Speed of radio waves `xx` time taken