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question_answer1) A vernier callipers has its main scale of 10 cm equally divided into 200 equal parts. Its vernier scale of 25 divisions coincides with 12 mm on the main scale. Find the least count (in mm) of the instrument.
question_answer2) In a vernier callipers, ten smallest divisions of the vernier scale are equal to nine smallest division on the main scale. If the smallest division on the main scale is half millimeter, then find the vernier constant. (in mm)
question_answer3) One centimetre on the main scale of vernier callipers is divided into ten equal parts. If 10 divisions of vernier scale coincide with 8 small divisions of the main scale, find the least count (in cm) of the callipers.
question_answer4) A vernier calliper has 20 divisions on the vernier scale, which coincide with 19 on the main scale. The least count of the instrument is 0.1 mm. The main scale divisions are of (in mm)?
question_answer5) The pitch of a screw gauge is 0.5 mm. its head scale contains 50 divisions. Find the least count (in mm) of the screw gauge.
question_answer6) The heat generated in a circuit is given by\[Q={{I}^{2}}Rt\], where I is current, R is resistance and t is time. If the percentage errors in measuring I, R and t are 2% , 1% and 1% respectively, then find the maximum error in measuring heat(in percentage)
question_answer7) The following observations were taken for determining surface tension of water by capillary tube method: Diameter of capillary,\[D=1.25\times {{10}^{-2}}m\] and rise of water in capillary, \[h=1.45\times {{10}^{-2}}m\]. Taking \[g=9.80m{{s}^{-2}}\]and using the relation \[T\text{ }=\text{ }\left( rgh/2 \right)\times {{10}^{3}}N{{m}^{-1}}\], what is the possible error in surface tension T? (in percentage)
question_answer8) The length of a cylinder is measured with the help of a vernier calipers whose smallest division on the main scale is 0.5 mm, and nine divisions of the main scale are equal to ten divisions of the vernier scale. It is observed that 78th divisions of the main scale coincides with the sixth division of the vernier scale. Calculate the length of the cylinder. (in cm)
question_answer9) The pitch of a screw gauge 0.5 mm and there are 50 divisions on the circular scale. In measuring the thickness of a metal plate, there are five divisions on the pitch scale (or main scale) and thirty fourth division coincides with the reference line. Calculate the thickness (in mm) of the metal plate.
question_answer10) The pitch of a screw gauge is 1mm and there are 100 divisions on its circular scale. When nothing is put in between its jaws, the zero of the circular scale lies 4 divisions below the reference line. When a steel wire is placed between the jaws, two main scale divisions are clearly visible and 67 division on the circular scale are observed. Determine the diameter (in mm) of the wire.
question_answer11) The main scale of a screw gauge in millimeter. The cap of the instrument is divided into 100 equal parts. Find the diameter (in mm) of a wire if no division on the main scale is completed and the cap has been moved through 37 divisions, the zero error being -3 division (in mm)
question_answer12) The main scale of a vernier calipers reads in millimeter and its vernier is divided into 10 divisions which coincide with 9 divisions of the main scale. When the two jaws of the instrument touch each other the seventh division of the vernier scale coincide with a scale division and the zero of the vernier lies to the right of the zero of main scale. Furthermore, when a cylinder is tightly placed along its length between the two jaws, the zero of the vernier scale lies slightly to the left of 3.2 cm; and the fourth vernier division coincides with a scale division. Calculate the measured length of the cylinder. (in cm)
question_answer13) The pitch of a screw gauge is 0.5 mm and there are 50 divisions on the circular scale. In measuring the thickness of a metal plate, there are five divisions on the pitch scale (or main scale) and thirty fourth division coincides with reference line. Calculate the thickness of the metal plate. (in mm)
question_answer14) The time period of oscillation of a simple pendulum is given by\[T=2\pi \sqrt{\ell /g}\]. The length of the pendulum is measured as\[\ell =10\pm 0.1cm\]and the time period as\[T=0.5\pm 0.02s\]. Determine percentage error in the value of g.
question_answer15) A physical quantity P is related to four observables A, B, C and D as\[P=4{{\pi }^{2}}{{A}^{3}}{{B}^{2}}/\left( \sqrt{C}D \right)\]. The percentage error of the measurement in A, B, C and D are 1%, 3% and 2%, 4% respectively. Determine the percentage error. Value of P is calculated 3.763.
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