Question

# The force is perpendicular to the ______.

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Solution

## Step 1: ForceAccording to Newton's second law of motion, force is directly proportional to the rate of change of momentum per unit of time.If $\stackrel{\to }{p}$ is the momentum and $t$ is the time taken, then force can be given as $\stackrel{\to }{F}\propto \frac{d\stackrel{\to }{p}}{dt}$.We know that $\stackrel{\to }{p}=m\stackrel{\to }{v}$, where $\stackrel{\to }{v}$ is the velocity.$\therefore \stackrel{\to }{F}=\frac{d}{dt}\left(m\stackrel{\to }{v}\right)=m\frac{d\stackrel{\to }{v}}{dt}$We know that acceleration $\stackrel{\to }{a}=\frac{d\stackrel{\to }{v}}{dt}$. Hence, $\stackrel{\to }{F}=m\stackrel{\to }{a}$.The derived unit of force is $kgm{s}^{-2}$ or $N$.Step 2: PressurePressure is defined as the force applied perpendicular to a surface per unit area.If $F$ is the force applied to a body and $A$ is the area upon which the force is applied, then the pressure can be given as, $P=\frac{F}{A}$The derived unit of pressure is $N{m}^{-2}$ and the SI unit is $Pa$.Hence, the force is perpendicular to the pressure.

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