(B) $1$. Torque $(\tau) = \text{Force} \times \text{distance} = [MLT^{-2}] \times [L] = [ML^2T^{-2}]$ (iv).$2$. Gravitational constant $(G) = \frac{Fr

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(B) $1$. Torque $(\tau) = \text{Force} \times \text{distance} = [MLT^{-2}] \times [L] = [ML^2T^{-2}]$ (iv).$2$. Gravitational constant $(G) = \frac{Fr^2}{m^2} = \frac{[MLT^{-2}][L^2]}{[M^2]} = [M^{-1}L^3T^{-2}]$ (iii).$3$. Capacitance $(C) = \frac{Q}{V} = \frac{[AT]}{[ML^2T^{-3}A^{-1}]} = [M^{-1}L^{-2}T^4A^2]$ $(i)$.$4$. Planck’s constant $(h) = \frac{E}{f} = \frac{[ML^2T^{-2}]}{[T^{-1}]} = [ML^2T^{-1}]$ (ii).Thus, the correct matching is $a-iv, b-iii, c-i, d-ii$.

Class 11 Physics Units, Dimensions and Measurement Mix Examples-Units, Dimensions and Measurement

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

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A
a - iv, b - ii, c - iii, d - i
B
a - iv, b - iii, c - i, d - ii
C
a - iv, b - i, c - iii, d - ii
D
a - ii, b - i, c - iii, d - iv

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Mix Examples-Units, Dimensions and Measurement

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It is estimated that each $cm^2$ of Earth receives about $2 \text{ calorie}$ of heat energy per minute from the Sun. This is called the solar constant. The value of the solar constant in $S.I.$ units is:

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Match List-$I$ with List-$II$.
List-$I$ List-$II$
$(A)$ Mass density $(I)$ $[ML^2T^{-3}]$
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$(C)$ Power $(III)$ $[ML^2T^0]$
$(D)$ Moment of inertia $(IV)$ $[ML^{-3}T^0]$
Choose the correct answer from the options given below:

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State,for each of the following physical quantities,if it is a scalar or a vector: volume,mass,speed,acceleration,density,number of moles,velocity,angular frequency,displacement,angular velocity.

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The units of length,velocity,and force are doubled. Which of the following is the correct change in the other units?

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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-$II$
$(A)$ Mass density	$(I)$ $[ML^2T^{-3}]$
$(B)$ Impulse	$(II)$ $[MLT^{-1}]$
$(C)$ Power	$(III)$ $[ML^2T^0]$
$(D)$ Moment of inertia	$(IV)$ $[ML^{-3}T^0]$

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It is estimated that each $cm^2$ of Earth receives about $2 \text{ calorie}$ of heat energy per minute from the Sun. This is called the solar constant. The value of the solar constant in $S.I.$ units is:

Match List-$I$ with List-$II$.List-$I$List-$II$$(A)$ Mass density$(I)$ $[ML^2T^{-3}]$$(B)$ Impulse$(II)$ $[MLT^{-1}]$$(C)$ Power$(III)$ $[ML^2T^0]$$(D)$ Moment of inertia$(IV)$ $[ML^{-3}T^0]$Choose the correct answer from the options given below:

The dimensions of pressure are equal to

State,for each of the following physical quantities,if it is a scalar or a vector: volume,mass,speed,acceleration,density,number of moles,velocity,angular frequency,displacement,angular velocity.

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Match List-$I$ with List-$II$.
List-$I$ List-$II$
$(A)$ Mass density $(I)$ $[ML^2T^{-3}]$
$(B)$ Impulse $(II)$ $[MLT^{-1}]$
$(C)$ Power $(III)$ $[ML^2T^0]$
$(D)$ Moment of inertia $(IV)$ $[ML^{-3}T^0]$
Choose the correct answer from the options given below: