4 questions from 2025
Figure.\( 1 \) shows the configuration of main scale and Vernier scale before measurement. Figure.\( 2 \) shows the configuration corresponding to the measurement of diameter \( D \) of a tube. The measured value of \( D \) is:
A single slit diffraction experiment is performed to determine the slit width using the equation, \( \dfrac{bd}{D} = m\lambda \), where \( b \) is the slit width, \( D \) the shortest distance between the slit and the screen, \( d \) the distance between the \( m^{\text{th}} \) diffraction maximum and the central maximum, and \( \lambda \) is the wavelength. \( D \) and \( d \) are measured with scales of least count of \( 1 \, \text{cm} \) and \( 1 \, \text{mm} \), respectively. The values of \( \lambda \) and \( m \) are known precisely to be \( 600 \, \text{nm} \) and \( 3 \), respectively. The absolute error (in \( \mu \text{m} \)) in the value of \( b \) estimated using the diffraction maximum that occurs for \( m = 3 \) with \( d = 5 \, \text{mm} \) and \( D = 1 \, \text{m} \) 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, \( \sigma \) the electrical conductivity and \( K \) 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 \( Z = \dfrac{S^{2}\sigma}{K} \) is:
Length, breadth and thickness of a strip having a uniform cross section are measured to be \( 10.5 \, \text{cm} \), \( 0.05 \, \text{mm} \), and \( 6.0 \, \mu\text{m} \), respectively. Which of the following option(s) give(s) the volume of the strip in \( \text{cm}^3 \) with correct significant figures:
