The period of a simple pendulum of length L feet is given by T=2πLg−−√~seconds. We assume that g, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is that of a clock that keeps good time when L=4 feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at L=4 feet.)

Given that,

The acceleration due to gravity on the surface of the earth = 32 feet/s²

We need to calculate the time

Using formula of time period

On differentiating with respect to l

Put the value into the formula

If the length of the pendulum is decreased to 3.97 feet.

We need  to calculate the time

Using formula of time period

Put the value into the formula

We need to calculate the gain time

Using formula for time

Put the value into the formula

Hence, The clock gain the time in 24 hours is 0.001 sec.

395.84

step-by-step explanation:

2πrh+2πr²

2 (pie)(radius)(height)+2(pie)(radius)^2