A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?

• 0.75 mm

• 0.80 mm

• 0.70 mm

• 0.70 mm

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

• A meter scale.

• A vernier calliper where the 10 divisions in vernier scale match with 9 division in the main scale and main scale have 10 divisions in 1 cm.

• A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.

• A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.

Let [ε₀] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then

• [ε₀] = [M^-1L^-3T²A]

• [ε₀] = [M^-1L^-3T⁴A²]

• [ε₀] =[M^-2L²T^-1A^-2]

• [ε₀] =[M^-2L²T^-1A^-2]

A spectrometer gives the following reading when used to measure the angle of a prism.
Main scale reading: 58.5 degree
Vernier scale reading: 09 divisions
Given that 1 division on the main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

• 58.59 degree

• 58.77 degree

• 58.65 degree

• 58.65 degree

A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm
Circular scale reading: 52 division
Given that 1 mm on the main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is

• 0.052 cm

• 0.026 cm

• 0.005

• 0.005

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10^–3 are

• 5,1,2

• 5,1,5

• 5,5,2

• 5,5,2

In an experiment, the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half–a–degree (= 0.5o° ), then the least count of the instrument is

• one minute

• half minute

• One degree

• One degree

The dimension of magnetic field in M, L, T and C (Coulomb) is given as

• MLT⁻¹C⁻¹

• MT²C⁻²

• MT⁻¹C⁻¹

• MT⁻¹C⁻¹

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is 

• 3.32 mm

• 3.73 mm

• 3.67 mm

• 3.67 mm

10.

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

• 3.32 mm 

• 3.73 mm

• 3.67 mm

• 3.67 mm