(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

Measurement of small distances:
(i) The screw gauge is an instrument used fro measuring accurately the dimensions of objects up to a maixmum of about 50 mm.
a. It is used for measuring external dimensions. i.e. diameter.
b. The least count of the screw gauge is 0.01 mm.
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 i.e. internal & external dimensions. The least count of vernier caliper is 0.1 mm
(ii) For measuring larger distances such as the height of a tree, distance of the Moon or a planet from the Earth, triangulation method, parallax meghod and radar method are used.
Triangulation method for the height of an accessible object:
a. Let `AB=h` be the height of the tree of tower to be measured. Let C be the point of observation at distanc x from B. Plance a range finder at C and measure the angle of elevation, `/_ACB=theta` as shown in figure.

b. From right angled triangle ABC, `tan theta=(AB)/(BC)=h/x` or height `h= x tan theta`
c. Knowing the distance x the height h can be determined.
RADAR method
(i) The word RADAR stands for radio detectiion and ranging.
(ii) 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.
(iii) BY measuring the tiem internval (t) between the instants the ratio waves are sent adn receiveced the distance of the planet can be determiend as
Distance `(d)=` Speed of radio waves `xx` time taken `d=(vxxt)/2`
(iv) Where v is the speed of the radio waves. As time taken (t) is for the distance covered during the forward and backward path of the radio wves, it is divided by 2 to get the actual distance of the object.
(v) This method can also be used to determine the height, at which an aeroplane flies from the groud.