Physics (Essay) Paper 2 WASSCE (SC), 2020

Question 4

 

 

The velocity v of a wave ina stretched string depends on the tension, T, in the spring and the mass per unit length μ of the spring. Obtain an expression for v in terms of T and μ, using the method dimensions.

Observation

 

 

This question was unpopular among candidates and the performance of the few that attempted it was poor.
 
The expected answer is:

Expression for v       

vα Tamb            OR
v = kTamb, k is dimensionless 
[v] = k[T]a[m]b
LT-1 = k(MLT-2)a(ML-1)b                   
LT-1 = kMa + bLa – bT-2a
For T,
-1 = -2a
a = ½            
For M,
0 = a + b
b = -a
= -½             
v = kT½m-½     
OR
v = k