(D) The dimensional formula for acceleration is $[M^0 L^1 T^{-2}]$.Using the conversion formula $n_2 = n_1 [L_1/L_2]^1 [T_1/T_2]^{-2}$.Given $n_1 = 10

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(D) The dimensional formula for acceleration is $[M^0 L^1 T^{-2}]$.Using the conversion formula $n_2 = n_1 [L_1/L_2]^1 [T_1/T_2]^{-2}$.Given $n_1 = 10$,$L_1 = 1\,m$,$T_1 = 1\,s$,$L_2 = 1\,km = 10^3\,m$,and $T_2 = 1\,hr = 3600\,s$.Substituting these values:$n_2 = 10 \times [1\,m / 10^3\,m]^1 \times [1\,s / 3600\,s]^{-2}$$n_2 = 10 \times [10^{-3}] \times [1/3600]^{-2}$$n_2 = 10 \times 10^{-3} \times (3600)^2$$n_2 = 10^{-2} \times 12960000$$n_2 = 129600$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

Medium

If the acceleration due to gravity is $10\,m/s^2$ and the units of length and time are changed to kilometer and hour respectively,the numerical value of the acceleration is

A
$360000$
B
$72000$
C
$36000$
D
$129600$

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Class 11

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Units, Dimensions and Measurement

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Dimensional Analysis, Uses and Limitations

If $P, Q$ and $R$ are physical quantities having different dimensions,which of the following combinations can never be a meaningful quantity?

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$A$ force $F$ acting on an object is given by $F = a \sqrt{x} - bt$,where $x$ is the distance in meters and $t$ is the time in seconds. The units of $a$ and $b$ are respectively:

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If the velocity of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are chosen as fundamental units,then the dimensions of mass in this new system are:

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If $x$ and $a$ represent distance,then for what value of $n$ is the given equation dimensionally correct? The equation is $\int \frac{dx}{\sqrt{a^2 - x^n}} = \sin^{-1} \frac{x}{a}$.

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If mass is written as $m=kc^{p} G^{-1 / 2} \,h^{1 / 2}$ then the value of $P$ will be : (Constants have their usual meaning with $k$ a dimensionless constant)

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If the acceleration due to gravity is $10\,m/s^2$ and the units of length and time are changed to kilometer and hour respectively,the numerical value of the acceleration is

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If $P, Q$ and $R$ are physical quantities having different dimensions,which of the following combinations can never be a meaningful quantity?

$A$ force $F$ acting on an object is given by $F = a \sqrt{x} - bt$,where $x$ is the distance in meters and $t$ is the time in seconds. The units of $a$ and $b$ are respectively:

If the velocity of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are chosen as fundamental units,then the dimensions of mass in this new system are:

If $x$ and $a$ represent distance,then for what value of $n$ is the given equation dimensionally correct? The equation is $\int \frac{dx}{\sqrt{a^2 - x^n}} = \sin^{-1} \frac{x}{a}$.

If mass is written as $m=kc^{p} G^{-1 / 2} \,h^{1 / 2}$ then the value of $P$ will be : (Constants have their usual meaning with $k$ a dimensionless constant)

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