If unit of force is 100,N , unit of length is 10,m and unit of time is 100,s , unit of m

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1.Units, Dimensions and Measurement

medium

If the unit of force is $100\,N$, unit of length is $10\,m$ and unit of time is $100\,s$ , what is the unit of mass in this system of units ?

Option A

Option B

Option C

Option D

Solution

${[\mathrm{F}]=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]=100 \mathrm{~N}}$
${[\mathrm{~L}]=10 \mathrm{~m}}$
${[\mathrm{~T}]=100 \mathrm{~s}}$
Substituting values of $\mathrm{L}$ and $\mathrm{T}$ from Eqs. (ii) and (iii) in Eq. (i), $\therefore \mathrm{M} \times 10 \times(100)^{-2}=100$
$\therefore \frac{\mathrm{M} \times 10}{100 \times 100}=100$
$\therefore \mathrm{M}=10^{5} \mathrm{~kg}$

Standard 11

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(AIPMT-1993)

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hard

(JEE MAIN-2021)

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easy

If the unit of force is $100\,N$, unit of length is $10\,m$ and unit of time is $100\,s$ , what is the unit of mass in this system of units ?

Solution

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Let us consider an equation

$\frac{1}{2} m v^{2}=m g h$

where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.