Question

If unit of length and time is doubled, the numerical value of g ( acceleration due to gravity) will be

Answer 1

It's a acceleration.
So, it's unit is = m/s^2
Now, according to the question, botha re doubled, so we have,
= 2m/(2s)^2
= 2m/4s^2
= 2/4 * m/s^2
= 1/2 * m/s^2.

Thus, numerical value of 'g'
= 1/2 * 9.8
= 4.9

The question is really good, it got me thinking for a while :)

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Answer 2

Given :

Unit of length and time is doubled .

To Find :

The numerical value of g .

Solution :

We know , acceleration due to gravity is :

$g=9.8\ m/s^2$ .

Let new unit of length is M = 2m .

Also , new unit of time be , S = 2s .

So ,

$g=9.8\ \dfrac{ \dfrac{M}{2}}{(\dfrac{S}{2})^2}\\\\g= 9.8\times 2\ M/S^2\\\\g=19.6\ M/S^2$

Hence , this is the required solution .

Learn More :

Units and measurements

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