Match List-$I$ with List-$II$ and select the correct answer.
List-$I$ List-$II$ $A$. Spring constant $1$. $M^1L^2T^{-2}$ $B$. Pascal $2$. $M^0L^0T^{-1}$ $C$. Hertz $3$. $M^1L^0T^{-2}$ $D$. Joule $4$. $M^1L^{-1}T^{-2}$
| List-$I$ | List-$II$ |
|---|---|
| $A$. Spring constant | $1$. $M^1L^2T^{-2}$ |
| $B$. Pascal | $2$. $M^0L^0T^{-1}$ |
| $C$. Hertz | $3$. $M^1L^0T^{-2}$ |
| $D$. Joule | $4$. $M^1L^{-1}T^{-2}$ |
- A$A-3, B-4, C-2, D-1$
- B$A-4, B-3, C-1, D-2$
- C$A-4, B-3, C-2, D-1$
- D$A-3, B-4, C-1, D-2$
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The maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its rotational kinetic energy $(K = \frac{1}{2} I \omega^{2})$. (in $\%$)
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View SolutionWhich of the following pairs have the same dimensions?
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View SolutionMatch the physical quantities given in List-$I$ with dimensions expressed in terms of mass $(M)$, length $(L)$, time $(T)$ and electric current $(A)$ given in List-$II$.
List-$I$ List-$II$ $(a)$ Torque $(i)$ $[M^{-1}L^{-2}T^4A^2]$ $(b)$ Gravitational constant (ii) $[M^1L^2T^{-1}]$ $(c)$ Capacitance (iii) $[M^{-1}L^3T^{-2}]$ $(d)$ Planck’s constant (iv) $[M^1L^2T^{-2}]$
| List-$I$ | List-$II$ |
| $(a)$ Torque | $(i)$ $[M^{-1}L^{-2}T^4A^2]$ |
| $(b)$ Gravitational constant | (ii) $[M^1L^2T^{-1}]$ |
| $(c)$ Capacitance | (iii) $[M^{-1}L^3T^{-2}]$ |
| $(d)$ Planck’s constant | (iv) $[M^1L^2T^{-2}]$ |
DifficultKCET 2026
View SolutionGive an example of:
$(a)$ a physical quantity which has a unit but no dimensions
$(b)$ a physical quantity which has neither unit nor dimensions
$(c)$ a constant which has a unit
$(d)$ a constant which has no unit
$(a)$ a physical quantity which has a unit but no dimensions
$(b)$ a physical quantity which has neither unit nor dimensions
$(c)$ a constant which has a unit
$(d)$ a constant which has no unit
Medium
View SolutionMatch 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) $M^0L^2T^{-2}$
| $(A)$ 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) $M^0L^2T^{-2}$ |
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