The diameter and height of a cylinder are mea | vedclass

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(B) The volume $V$ of a cylinder is given by $V = \pi R^2 h = \frac{\pi}{4} D^2 h$.Given $D = 12.6\, cm$,$\Delta D = 0.1\, cm$,$h = 34.2\, cm$,and $\D

Vedclass · Accepted Answer

$4260 \pm 80\, cm^3$

Vedclass · Answer

(B) The volume $V$ of a cylinder is given by $V = \pi R^2 h = \frac{\pi}{4} D^2 h$.Given $D = 12.6\, cm$,$\Delta D = 0.1\, cm$,$h = 34.2\, cm$,and $\Delta h = 0.1\, cm$.First,calculate the volume: $V = \frac{3.14159}{4} 	imes (12.6)^2 	imes 34.2 \approx 4264.4\, cm^3$.Rounding to appropriate significant figures (three significant figures based on the given data),$V = 4260\, cm^3$.Now,calculate the relative error: $\frac{\Delta V}{V} = 2\frac{\Delta D}{D} + \frac{\Delta h}{h}$.$\Delta V = V 	imes (2 	imes \frac{0.1}{12.6} + \frac{0.1}{34.2}) = 4264.4 	imes (0.01587 + 0.00292) \approx 4264.4 	imes 0.01879 \approx 80.13$.Rounding the absolute error to one significant figure,we get $\Delta V = 80\, cm^3$.Thus,the volume is $V = 4260 \pm 80\, cm^3$.

List $I$ (Physical Quantity)	List $II$ (Dimensional Formula)
$(A)$ Pressure gradient	$(I)$ $[M^0 L^2 T^{-2}]$
$(B)$ Energy density	$(II)$ $[M^1 L^{-1} T^{-2}]$
$(C)$ Electric Field	$(III)$ $[M^1 L^{-2} T^{-2}]$
$(D)$ Latent heat	$(IV)$ $[M^1 L^1 T^{-3} A^{-1}]$

List-$I$	List-$II$
$(a)$ ${R}_{H}$ (Rydberg constant)	$(i)$ ${kg} {m}^{-1} {s}^{-1}$
$(b)$ $h$ (Planck's constant)	$(ii)$ ${kg} {m}^{2} {s}^{-1}$
$(c)$ $u_{B}$ (Magnetic field energy density)	$(iii)$ ${m}^{-1}$
$(d)$ $\eta$ (Coefficient of viscosity)	$(iv)$ ${kg} {m}^{-1} {s}^{-2}$

$(A)$ Thermal conductivity	$(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant	(ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat	(iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat	(iv) $M^0L^2T^{-2}$

The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1\, cm$ and $34.2 \pm 0.1\, cm$,respectively. What will be the value of its volume in appropriate significant figures?

Similar Questions

Match the following physical quantities with their respective dimensional formulas:
$(A)$ Thermal conductivity $(i)$ $MLT^{-3}K^{-1}$
$(B)$ Boltzmann constant (ii) $M^0L^2T^{-2}K^{-1}$
$(C)$ Latent heat (iii) $ML^2T^{-2}K^{-1}$
$(D)$ Specific heat (iv) $M^0L^2T^{-2}$

The mechanical equivalent of heat $J$ is

Which quantity among the following has neither units nor dimensions?

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