Find an expression for the time period 'T' of a simple pendulum. The time
period 'T' may depend upon (i) mass 'm' of the bob of the pendulum, (ii) length
'l of pendulum, (iii) acceleration due to gravity 'g' at the place where the
pendulum is suspended.
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Answer:
T proportional to mass , length , acceleration
let mass , m raise to a
length , l raise to b
acceleration due to gravity g raise to c
dimension of mass= M^1
dimension of length=L^1
dimension of gravity=L^1T^-2
T=k × M^a × L^b × LT^-2C
MASS , 0=a
Length , 0=b+c
Time , 1= -2c
c= -1/2
therefore , 0=b - 1/2
b= 1/2
therefore , T proportional to M^0 L^-1/2 G^-1/2
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