Question

Find expression of time period of a simple pendulum with dimensional analysis, given that time period
of simple pendulum depends on length of pendulum land gravitational acceleratio g.​

Answer 1

Answer:

Explanation:

Since it is given that time period of a simple pendulum depends upon the length of pendulum (l) and acceleration due to gravity (g).

So,

T=f(l,g)

....................(1)

where alpha is the sign of proportionality.

we know the dimension formula for l and g.

for l=L and  

Now,

Compare the power of L and T.

a+b=0........................(1),-2b=1.........................(2)

from (2) we get

from (1) we get

put a and b in (1) we get