dynamics/kinematics questions

[kdgamz]

heres another..i have no clue about this question except for the fact that you need to use standard units

Question 3

The period T seconds of a pendulum is known to vary with some power of its length,
l metres, some power of its mass, m grams and some power of its acceleration due to
gravity, g m/s2. Use the equality of dimensions method to find a variance expression
for T.

thanks

[biggzee]

heres another..i have no clue about this question except for the fact that you need to use standard units

Question 3

The period T seconds of a pendulum is known to vary with some power of its length,
l metres, some power of its mass, m grams and some power of its acceleration due to
gravity, g m/s2. Use the equality of dimensions method to find a variance expression
for T.

thanks

All of your units should be equal on each side of the variation/ equality sign.

T = k* L^(p) * M^(q) * g^(r)   (T- period, L - length, M - mass, g -accel. due to grav., k p q and r are constants)
= [1]*[m^p][kg^q][m^r*s^-2r]     k is dimensionless
-2r = 1 (r= -1/2), as it is the only expression on the RHS involving the unit of time
= [m^p][kg^q][m^-0.5 * s]
p - 0.5 = 0 (p=0.5), as m^p and m^0.5 are multiplied to give a unit free of length.
and q=0, as the LHS has no mass component.

therefore T is proportional to L^0.5 * g^-0.5