Units and Measurements

In a new system of units, the units of mass, length, time and current are 5 kg, 5 m, 5 s and 5 A, respectively. If 0 and 0 are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of 0/ 0, is:

Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm, 0.05 mm, and 6.0 , respectively. Which of the following option(s) give(s) the volume of the strip in cm3 with correct significant figures:

1. 3.2 10-5
2. 32.0 10-6
3. 3.0 10-5
4. 3 10-5

A single slit diffraction experiment is performed to determine the slit width using the equation, bdD=m , where b is the slit width, D the shortest distance between the slit and the screen, d the distance between the mth diffraction maximum and the central maximum, and is the wavelength. D and d are measured with scales of least count of 1 cm and 1 mm, respectively. The values of and m are known precisely to be 600 nm and 3, respectively. The absolute error (in m) in the value of b estimated using the diffraction maximum that occurs for m=3 with d=5 mm and D=1 m is

A temperature difference can generate e.m.f. in some materials. Let S be the e.m.f. produced per unit temperature difference between the ends of a wire, the electrical conductivity and the thermal conductivity of the material of the wire. Taking M, L, T, I and K as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity Z= S2 is:

1. [M0L0T0I0K0]
2. [M0L0T0I0K-1]
3. [M1L2T-2I-1K-1]
4. [M1L2T-4I-1K-1]

A dimensionless quantity is constructed in terms of electronic charge e, permittivity of free space 0, Planck's constant h, and speed of light c. If the dimensionless quantity is written as e 0 h c and n is a non-zero integer, then ( , , , ) is given by

1. (2n,-n,-n,-n)
2. (n,-n,-2n,-n)
3. (n,-n,-n,-2n)
4. (2n,-n,-2n,-2n)

The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in the determination of the volume is .