Physics

Problem

A student writes the expression

T = 2\pi \sqrt{\,l\,g\,}

for the time period

T

of a simple pendulum of length

l

oscillating under gravity

g

. a. (i) Verify whether the given expression is dimensionally consistent. b. (ii) Assuming that

T

depends only on

l

and

g

, obtain the corrected functional form of

T

. Keep an undetermined dimensionless constant

K

in your result. c. (iii) Taking

K = 2\pi

, calculate the time period for

l = 0.64\,\text{m}

and

g = 9.8\,\text{m\,s}^{-2}

. Round off your answer to two significant figures.