Question

A clock which has brass pendulum beats correctly at 30C will it run faster or slower if temperature increase or decrease​

Answer 1

A brass pendulum clock will run slower in the summer due to thermal expansion, which lengthens the pendulum, and faster in the winter when the pendulum contracts. If moved to a location with stronger gravity, the pendulum must be lengthened to keep correct time.

Step-by-step explanation:

The functioning of a pendulum clock is affected by changes in temperature since the length of the pendulum will alter due to thermal expansion. In the context of a brass pendulum, brass expands when the temperature increases, making the pendulum longer. A longer pendulum has a longer period, meaning it swings slower than required. Therefore, in the summer, when the temperature is higher, the clock will run slower because the pendulum takes more time to complete each swing.

In contrast, as the temperature decreases in the winter, the brass contracts, leading to a shorter pendulum. A shorter pendulum has a shorter period and swings faster. Hence, the clock will run faster in the winter.

If the acceleration due to gravity is greater in a new location to which the pendulum clock is moved, the pendulum would need to be lengthened. A longer pendulum compensates for the greater gravitational pull to maintain the accurate timing.

Answer 2

We know that the period of a pendulum is written as:

T = 2*pi*√(L/g)

where:

g = gravitational acceleration = 9.8m/s^2

pi = 3.1415...

L = length of the pendulum, in this case, is the length of the brass pendulum.

Now, we know that the brass dilates when the temperature increases.

Then if the temperature increases, the value of L will increase, which means that the period T will also increase, because L is in the numerator of T.

If the period increases the complete motion of the pendulum needs more time, this would mean that the clock will run slower.

If the temperature decreases, the opposite occurs, the value of L decreases, and then the period also decreases, which means that the clock will run faster.