Question
Fill in the blanks by suitable conversion of units: $G = 6.67 \times 10^{-11} N m^2 (kg)^{-2} = .... (cm)^3 s^{-2} g^{-1}$
✓
Answer
$G = 6.67 \times 10^{–11} N m^2 (kg)^{–2} = 6.67 \times 10^{–8} (cm)^3s^{–2} g^{–1}.$
Given, $G = 6.67 \times 10^{–11} N m^2 (kg)^{–2} $ We know that $1N = 1kg m s^{-2}$
$1kg = 10^3g 1m = 100cm = 10^2cm$ Putting above values,
we get $6.67 \times 10^{–11} N m^2kg^{–2}$
$= 6.67 \times 10^{–11} \times (1kg m s^{–2}) (1m^2) (1Kg^{–2})$ Solve and cancel out the units we get
$\Rightarrow 6.67 \times 10^{–11} \times (1kg^{–1} \times 1m^3 \times 1s^{–2})$ Putting above values to convert Kg to g and m to cm
$\Rightarrow 6.67 \times 10^{–11} \times (10^3g)^{-1} \times (10^2cm)^3 \times (1s^{–2})$
$\Rightarrow 6.67 \times 10^{–11} \times 10^{-3}g^{-1} \times 10^6cm^3 \times (1s^{–2})$
$\Rightarrow 6.67 \times 10^{–8}cm^3 s^{–2} g^{–1}$
$G = 6.67 \times 10^{–11} N m^2 (kg)^{–2}$
$= 6.67 \times 10^{–8} (cm)^3s^{–2} g^{–1}.$
Given, $G = 6.67 \times 10^{–11} N m^2 (kg)^{–2} $ We know that $1N = 1kg m s^{-2}$
$1kg = 10^3g 1m = 100cm = 10^2cm$ Putting above values,
we get $6.67 \times 10^{–11} N m^2kg^{–2}$
$= 6.67 \times 10^{–11} \times (1kg m s^{–2}) (1m^2) (1Kg^{–2})$ Solve and cancel out the units we get
$\Rightarrow 6.67 \times 10^{–11} \times (1kg^{–1} \times 1m^3 \times 1s^{–2})$ Putting above values to convert Kg to g and m to cm
$\Rightarrow 6.67 \times 10^{–11} \times (10^3g)^{-1} \times (10^2cm)^3 \times (1s^{–2})$
$\Rightarrow 6.67 \times 10^{–11} \times 10^{-3}g^{-1} \times 10^6cm^3 \times (1s^{–2})$
$\Rightarrow 6.67 \times 10^{–8}cm^3 s^{–2} g^{–1}$
$G = 6.67 \times 10^{–11} N m^2 (kg)^{–2}$
$= 6.67 \times 10^{–8} (cm)^3s^{–2} g^{–1}.$
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