Question

The clock pendulum consists of the slender rod of length ( l ) and mass ( m ) and the bob of mass ( 7m ). Neglecting the effects of the radius of the bob, determine ( l_0 ) in terms of the bob position ( x ). Calculate the ratio ( r ) of ( l_0 ) evaluated for ( x ).

a. ( l_0 = x ), ( r = 1 )
b. ( l_0 = 2x ), ( r = 2 )
c. ( l_0 = √2x ), ( r = √2 )
d. ( l_0 = x2 ), ( r = 0.5 )

Answer 1

The length of the clock pendulum in terms of the bob position is equal to x, and the ratio of l0 evaluated for x is 1. The correct answer is A

Step-by-step explanation:

To determine the relationship between the effective length (l0) of the clock pendulum and the position of the bob (x), we use the equation:

l0 = I / (mx) + x

Here:

l0 is the effective length of the pendulum.

I represents the moment of inertia of the compound pendulum.

m is the mass of the slender rod.

x is the position of the bob.

Now, let's calculate the ratio (r) for different scenarios:

a. If l0 = x:

r = l0 / x = 1

b. If l0 = 2x:

r = l0 / x = 2

c. If l0 = √2x:

r = l0 / x = √2

d. If l0 = x^2:

r = l0 / x = x

Upon evaluating these expressions, the correct choice is indeed (a) l0 = x and r = 1. This implies that when the effective length l0 is equal to the bob's position x, the ratio r is 1.