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The smallest division on the main scale of a Vernier calipers is \( 0.1 \, \text{cm} \). Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere 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:

A physical quantity \( \vec{S} \) is defined as \( \vec{S} =( \vec{E} \times \vec{B}) / \mu_{0} \), where \( \vec{E} \) is electric field, \( \vec{B} \) is magnetic field and \( \mu_{0} \) is the permeability of free space. The dimension of \( \vec{S} \) are the same as the dimensions of which of the following quantity(ies)?