Match the following?Column-IColumn-II(a) Rati | vedclass

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(D) The time period of a simple pendulum is $T = 2\pi \sqrt{\frac{L}{g}}$. The fractional change in time period due to temperature change $\Delta T$ i

Vedclass · Accepted Answer

$(a-iv), (b-iii), (c-ii), (d-i)$

Vedclass · Answer

(D) The time period of a simple pendulum is $T = 2\pi \sqrt{\frac{L}{g}}$. The fractional change in time period due to temperature change $\Delta T$ is $\frac{\Delta T}{T} = \frac{1}{2} \alpha \Delta T$. Thus, $(a) - (iv)$.$(b)$ The ratio of the actual length to the scale reading is given by the factor $(1 + \alpha \Delta T)$ due to thermal expansion of the scale. Thus, $(b) - (iii)$.$(c)$ For an ideal gas at constant pressure, the coefficient of volume expansion $\gamma = \frac{1}{T}$. Therefore, the reciprocal is $T$. Thus, $(c) - (ii)$.$(d)$ From Hooke's Law, $\frac{F}{A} = Y \frac{\Delta L}{L}$, so $\frac{F}{YA} = \frac{\Delta L}{L} = \alpha \Delta T$. Thus, $(d) - (i)$.Combining these, the correct match is $(a-iv), (b-iii), (c-ii), (d-i)$.

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	$(iii) \, (1 + \alpha \Delta T)$
$(d) \, \frac{F}{YA} =$	$(iv) \, \frac{1}{2} \alpha \Delta T$

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) $[M^{-1} L^3 T^{-2}]$

Column $I$	Column $II$
$(A)$ $GM_e M_s$ ($G$: universal gravitational constant,$M_e$: mass of the earth,$M_s$: mass of the Sun)	$(p)$ $(\text{volt})(\text{coulomb})(\text{metre})$
$(B)$ $\frac{3RT}{M}$ ($R$: universal gas constant,$T$: absolute temperature,$M$: molar mass)	$(q)$ $(\text{kg})(\text{m})^3(\text{s})^{-2}$
$(C)$ $\frac{F^2}{q^2 B^2}$ ($F$: force,$q$: charge,$B$: magnetic field)	$(r)$ $(\text{m})^2(\text{s})^{-2}$
$(D)$ $\frac{GM_e}{R_e}$ ($G$: universal gravitational constant,$M_e$: mass of the earth,$R_e$: radius of the earth)	$(s)$ $(\text{farad})(\text{volt})^2(\text{kg})^{-1}$

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