Question

A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10°C and coefficient of linear expansion of the metal of the rod is 2 × 10⁶ °C^-1, the period of pendulum will increased by ______.

Options

• 1 × 10^-3%

• -1 × 10^-3%

• 2 × 10^-3%

• -2 × 10^-3%

Answer 1

A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10°C and coefficient of linear expansion of the metal of the rod is 2 × 10⁶ °C^-1, the period of pendulum will increased by 1 × 10^-3%.

Explanation:

we know that = 2π`sqrt(("l"//"g"))`

∴ ΔT = `(2pi)/2(1/"lg")^(1//2)`

Δl or `(Delta"T")/"T"=(Delta"l")/(2"l")=1/2alphaDelta"t"` 

= `((2xx10^-6)(10))/2`

= 1 × 10^-5

or `(Delta"T")/"T"xx100=1xx10^-5xx100`

= 1 × 10^-3%