Medium
State whether the following statements are true or false:
$(a)$ $A$ dimensionally incorrect equation can be correct.
$(b)$ $1 \ AU = 9.46 \times 10^{15} \ m$
$(c)$ The dimensional formula of force and stress are the same.
$(d)$ The dimensions of a physical quantity are different in different systems of units.
$(a)$ $A$ dimensionally incorrect equation can be correct.
$(b)$ $1 \ AU = 9.46 \times 10^{15} \ m$
$(c)$ The dimensional formula of force and stress are the same.
$(d)$ The dimensions of a physical quantity are different in different systems of units.
(NONE) False. $A$ dimensionally incorrect equation must be physically incorrect.
$(b)$ False. $1 \ AU = 1.496 \times 10^{11} \ m$. The value $9.46 \times 10^{15} \ m$ represents $1 \ \text{light year}$.
$(c)$ False. The dimensional formula of force is $[M^1 L^1 T^{-2}]$, while the dimensional formula of stress (force per unit area) is $[M^1 L^{-1} T^{-2}]$.
$(d)$ False. The dimensions of a physical quantity are independent of the system of units used; only the numerical value changes.
$(b)$ False. $1 \ AU = 1.496 \times 10^{11} \ m$. The value $9.46 \times 10^{15} \ m$ represents $1 \ \text{light year}$.
$(c)$ False. The dimensional formula of force is $[M^1 L^1 T^{-2}]$, while the dimensional formula of stress (force per unit area) is $[M^1 L^{-1} T^{-2}]$.
$(d)$ False. The dimensions of a physical quantity are independent of the system of units used; only the numerical value changes.
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Similar Questions
Which of the following statements is incorrect?
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:
| 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 | $(IV)$ $[ML^{-3}T^0]$ |
The density of a substance is $4 \, g/cc$ in a system in which the unit of length is $5 \, cm$ and the unit of mass is $20 \, g$. The density of the substance in the $CGS$ system is: (in $units$)
Of the following quantities,which one has dimensions different from the remaining three?
MediumAIIMS 1987
View SolutionThe coefficients of thermal expansion of steel and a metal $X$ are respectively $12 \times 10^{-6} /^{\circ}C$ and $2 \times 10^{-6} /^{\circ}C$. At $40^{\circ}C$,the side of a cube of metal $X$ was measured using a steel vernier callipers. The reading was $100 \, mm$. Assuming that the calibration of the vernier was done at $0^{\circ}C$,then the actual length of the side of the cube at $0^{\circ}C$ will be:
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