Match the following?
Column-$I$Column-$II$
$(a)$ Ratio of change in time period of a simple pendulum with temperature to its original time period$(i) \, \alpha \Delta T$
$(b)$ Ratio of the value of a length to its scale reading$(ii) \, T$
$(c)$ Reciprocal of coefficient of volume expansion for an ideal gas of constant pressure$(iii) \, (1 + \alpha \Delta T)$
$(d) \, \frac{F}{YA} =$$(iv) \, \frac{1}{2} \alpha \Delta T$

  • A
    $(a-iv), (b-ii), (c-i), (d-ii)$
  • B
    $(a-iii), (b-iv), (c-ii), (d-i)$
  • C
    $(a-iv), (b-i), (c-ii), (d-iii)$
  • D
    $(a-iv), (b-iii), (c-ii), (d-i)$

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Similar Questions

Some physical constants are given in List-$I$ and their dimensional formulae are given in List-$II$. Match the following:
List-$I$List-$II$
$(1)$ Planck's constant$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity(iv) $[M^{-1} L^3 T^{-2}]$

The correct answer is:

Which of the following pairs of physical quantities have the same dimensions,where one is a vector and the other is a scalar?

The unit of length convenient on the atomic scale is known as an $\mathring{A}$ and is denoted by $\mathring{A}: 1 \mathring{A} = 10^{-10} \, m$. The size of a hydrogen atom is about $0.5 \mathring{A}$. What is the total atomic volume in $m^{3}$ of a mole of hydrogen atoms?

The diameter of a wire measured by a screw gauge of least count $0.001 \text{ cm}$ is $0.08 \text{ cm}$. The length measured by a scale of least count $0.1 \text{ cm}$ is $150 \text{ cm}$. When a weight of $100 \text{ N}$ is applied to the wire, the extension in length is $0.5 \text{ cm}$, measured by a micrometer of least count $0.001 \text{ cm}$. The error in the measured Young's modulus is $\alpha \times 10^9 \text{ N/m}^2$. The value of $\alpha$ is . . . . . . . (Ignore the contribution of the load to Young's modulus error calculation)

Fill in the blanks:
$(a)$ $\frac{1\,\mu m}{1\,fm} = \,....$
$(b)$ The number of significant figures in $0.0060$ is $....$
$(c)$ To study nanotechnology,the $....$ microscope has been developed.

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