Question

if the unit of force is considered as 200 newton and that of power is 10^8W and that of time is 1 millisecond then find out the unit of length​

Answer 1

First we have to express length $\sf{L}$ in terms of force $\sf{F,}$ power $\sf{P,}$ and time $\sf{t.}$

We can use dimensional method directly but it's avoided here as it takes much time. So an alternate method is used here.

We know that power is work done per unit time.

$\displaystyle\longrightarrow\sf{P=\dfrac{W}{t}}$

And we know work is the (dot) product of force and displacement. So,

$\displaystyle\longrightarrow\sf{P=\dfrac{F\,s}{t}}$

Well, displacement is nothing but a length. Then we have,

$\displaystyle\longrightarrow\sf{P=\dfrac{F\,L}{t}}$

Hence the length is,

$\displaystyle\longrightarrow\sf{L=\dfrac{P\,t}{F}}$

Now we have expressed length in terms of force, power and time, whose new units mentioned are given below.

• $\displaystyle\sf{F=200\ N}$

• $\sf{P=10^8\ W}$

• $\sf{t=1\ ms=10^{-3}\ s}$

Hence the new unit of length is,

$\displaystyle\longrightarrow\sf{L=\dfrac{10^8\times10^{-3}}{200}}$

$\longrightarrow\sf{\underline{\underline{L=500\ m}}}$

Answer 2

Answer:

First we have to express length \sf{L}L in terms of force \sf{F,}F, power \sf{P,}P, and time \sf{t.}t.

We can use dimensional method directly but it's avoided here as it takes much time. So an alternate method is used here.

We know that power is work done per unit time.

\displaystyle\longrightarrow\sf{P=\dfrac{W}{t}}⟶P=

t

W

And we know work is the (dot) product of force and displacement. So,

\displaystyle\longrightarrow\sf{P=\dfrac{F\,s}{t}}⟶P=

t

Fs

Well, displacement is nothing but a length. Then we have,

\displaystyle\longrightarrow\sf{P=\dfrac{F\,L}{t}}⟶P=

t

FL

Hence the length is,

\displaystyle\longrightarrow\sf{L=\dfrac{P\,t}{F}}⟶L=

F

Pt

Now we have expressed length in terms of force, power and time, whose new units mentioned are given below.

\displaystyle\sf{F=200\ N}F=200 N

\sf{P=10^8\ W}P=10

8

W

\sf{t=1\ ms=10^{-3}\ s}t=1 ms=10

−3

s

Hence the new unit of length is,

\displaystyle\longrightarrow\sf{L=\dfrac{10^8\times10^{-3}}{200}}⟶L=

200

10

8

×10

−3

\longrightarrow\sf{\underline{\underline{L=500\ m}}}⟶

L=500 m