Physics

Problem

The time period

T

of a simple pendulum may depend on its length

l

, the mass of the bob

m

and the acceleration due to gravity

g

. Four students propose the following possible relationships: (a)

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

(b)

T = 2\pi \sqrt{\dfrac{m l}{g}}

(c)

T = 2\pi \sqrt{\dfrac{l g}{m}}

(d)

T = 2\pi \sqrt{\dfrac{m}{l g}}

(i) Using dimensional considerations, identify the expression that can be correct. (ii) For the correct expression, calculate the time period when

l = 0.64\,\text{m}

and

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

. a. (i) Identify the dimensionally correct expression. b. (ii) Calculate

T

for

l = 0.64\,\text{m}

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