#calculate the percentage error
#Given:
l=9.3; # length in cm
b=8.5;# breadth in cm
h=5.4;# height in cm
#calculations
V= l*b*h; # Volume in cm**3
delta_l = 0.1; delta_b = 0.1; delta_h = 0.1; # scale has a least count = 0.1 cm
# absolute error
delta_V = (b*h*delta_l + l*h*delta_b +l*b*delta_h); # in cm**3
#relative error
re = delta_V/V;
p= re*100; # Evaluating percentage error
#results
print "Percentage Error (percentage) = ",round(p,0)
#calculate the percentage error
#Given :
M= 10.0; #weight in g
V= 5.80;#volume in cm**3
#calculations
Rho = M/V; # Density in g/cm**3
delta_M= 0.2 # apparatus has a least count of 0.2 g
delta_V= 0.05# apparatus has a least count of 0.05 cm**3
delta_Rho = (delta_M/V) +((M*delta_V)/V**2);# absolute error in g/cm**3
re = delta_Rho/Rho ; #Evaluating Relative Error
p = re*100;# Evaluating Percentage Error
#results
print "Percentage error (percentage) = ",round(p,2)
print'Result obtained differs from that in textbook, because delta_M walue is taken 0.1 g , instead of 0.2 g as mentioned in the problem statement.'
#calculate the Actual val of c/r ranges and percentage error
#Given:
#(a)
import math
lc = 0.1# least count in cm
c = 6.9 #Circumference c in cm
r= 1.1 # radius of circle in cm
val =2*math.pi;
# Circumference,c= 2*pi*r or c/r = 2*pi
# Error in c/r is , delta(c/r)= [(c/r**2)+(1/r)](LC/2) , LC is Least Count .
E= ((c/r**2)+(1./r))*(lc/2.);#Error in c/r is delta(c/r)
ob = c/r; # Observed Value
#Actual Value of c/r ranges between
ac1 = ob-E;# Evaluating Minimum value for c/r
ac2 = ob+E;# Evaluating Maximum value for c/r
p = (E/ob)*100.; #Evaluating percentage error
#results
print "(a)Actual Value of c/r ranges between",round(ac1,1), "-",round(ac2,1)," and Percentage error =",round(p,1)," percentage. "
#(b)
lc1 = 0.001;#Now the least count is 0.001 cm
c1 = 6.316;#Circumference in cm
r1=1.005;#Circle radius in cm
E1 =((c1/r1**2) + (1/r1))*(lc1/2); # Error in c/r is delta(c/r)
ob1= c1/r1; #Observed Value
p1=(E1/ob1)*100.;#Evaluating percentage error
#Actual Value of c/r ranges between
a1= ob1-E1;#Evaluating Minimum value for c/r
a2= ob1+E1;#Evaluating Maximum value for c/r
print "(b)Actual Value of c/r ranges between",round(a1,3),"-",round(a2,3),"and Percentage error =",round(p1,2)," percentage."
#calculate the percentage lower or higher than experimental value
#Given
import math
# (a) Newton's Theory
# v= (P/rho)**2 , P= Pressure , rho = density
P = 76.; # 76 cm of Hg pressure
V= 330. ; # velocity of sound in m/s
rho = 0.001293; # density for dry air at 0 degrees celsius in g/cm**3
g = 980.;#gravitational acceleration in cm/s**2
#Density of mercury at room temperature is 13.6 g/cm**3
# 1 cm**2 = 1.0*10**-4 m**2
#calculations
v = math.sqrt(((P*13.6*g)/rho)*10**-4); # velocity of sound in m/s
p= ((V-v)/V)*100; # % lower than the experimental value
#results
print "(a) It is is",round(p,0)," percentage lower than the experimental value."
# (b) Laplace's Theory
# v= ((gama*P)/rho)**2., gamma = adiabatic index Thus,
#Given :
gama = 1.41 # Adiabatic index
#Density of mercury at room temperature is 13.6 g/cm**3
# 1 cm**2 = 1.0*10**-4 m**2
v1 = math.sqrt(((gama*P*13.6*g)/rho)*10**-4);# velocity of sound in m/s
p1 = ((V-round(v1))/V)*100;# % higher than the eperimental value
#results
print "(b) It is",round(abs(p1),1),"percentage higher than the experimental value."