Medium
In a new system,the unit of mass is $10 \ kg$,the unit of length is $5 \ m$,and the unit of time is $10 \ s$. Then,in this new system,$20 \ g/cm^3$ is equal to:
- A$2.5 \times 10^2$ new units
- B$2.5 \times 10^4$ new units
- C$2.5 \times 10^5$ new units
- D$2.5 \times 10^3$ new units
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Which physical quantities have the same dimension?
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View SolutionFind the rate of change of the volume of a sphere with respect to its surface area when the radius is $2 \ cm$.
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View SolutionMatch the List-$I$ with List-$II$. The correct match in the following is:
List-$I$
List-$II$
$A$. Boltzmann constant
$I$. $[ML^0T^0]$
$B$. Coefficient of viscosity
$II$. $[ML^{-1}T^{-1}]$
$C$. Water equivalent
$III$. $[ML^2T^{-2}K^{-1}]$
$D$. Coefficient of thermal conductivity
$IV$. $[MLT^{-3}K^{-1}]$
| List-$I$ | List-$II$ |
| $A$. Boltzmann constant | $I$. $[ML^0T^0]$ |
| $B$. Coefficient of viscosity | $II$. $[ML^{-1}T^{-1}]$ |
| $C$. Water equivalent | $III$. $[ML^2T^{-2}K^{-1}]$ |
| $D$. Coefficient of thermal conductivity | $IV$. $[MLT^{-3}K^{-1}]$ |
Match the following (Take the relative strength of the strongest fundamental forces in nature as $1$):
$I$ (Fundamental forces in nature) $II$ (Relative strength) $(A)$ Strong nuclear force $(e)$ $10^{-2}$ $(B)$ Weak nuclear force $(f)$ $1$ $(C)$ Electromagnetic force $(g)$ $10^{10}$ $(D)$ Gravitational force $(h)$ $10^{-13}$ $(i)$ $10^{-39}$
The correct match is:
| $I$ (Fundamental forces in nature) | $II$ (Relative strength) |
|---|---|
| $(A)$ Strong nuclear force | $(e)$ $10^{-2}$ |
| $(B)$ Weak nuclear force | $(f)$ $1$ |
| $(C)$ Electromagnetic force | $(g)$ $10^{10}$ |
| $(D)$ Gravitational force | $(h)$ $10^{-13}$ |
| $(i)$ $10^{-39}$ |
The correct match is:
Some physical quantities are given in Column $I$ and some possible $SI$ units in which these quantities may be expressed are given in Column $II$. Match the physical quantities in Column $I$ with the units in Column $II$.
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) $(s)$ $(\text{farad})(\text{volt})^2(\text{kg})^{-1}$
| 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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