part 1 of 2 10 points This problem shows how dimensional anal- ysis helps us che

Question

part 1 of 2 10 points This problem shows how dimensional anal- ysis helps us check and sometimes even find a formula A rope has a cross section A-9.76 m2 and density ? 1670 kg/m3. The "linear" density ofthe rope defined to be the mass per unit length, can be written in the form ? Based on dimensional analysis, determine the powers z and y by choosing an expression below. 2.A A2 A2 Question 14, chap 101, sect 6. part 2of 2 10 points A simple pendulum is made out of a string with length L and a mass m attached to one end of the string. Its period T of oscillation may depend on the gravitational acceleration g, and also depend on L and m. Based on dimensional analysis, check which one of the following expressions is dimension- ally acceptable, where k is a dimensionless constant

Explanation / Answer

(1) We know that the dimension of the linear density (u) is= kg/m
Dimension of density (p) = kg/m3
Dimension of area (A) = m2
Now the formula is
u = pxAy
Putting the dimension of the above variable
(kg/m) = (kg/m3)x(m2)y
kgm-1 = kgxm2y-3x
Now on compairing the dimension on both side
x =1
2y-3x = -1
2y-3(1)= -1
2y = -1+3 = 2
y = 1
Therfore the formula will be
u = pA
hence the correct expression is 9.

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