Question

A clock pendulum having coefficient of linear expansion. α = 9 × 10^-7/°C^-1 has a period of 0.5 s at 20°C. If the clock is used in a climate, where the temperature is 30°C, how much time does the clock lose in each oscillation? (g = constant)

विकल्प

• 2.5 × 10^-7 s

• 5 × 10^-7 s

• 1.125 × 10^-6 s

• 2.25 × 10^-6 s

Answer 1

2.25 × 10^-6 s

Explanation:

Given, the coefficient of linear expansion,

α = 9 × 10^-7/°C^-1 

Initial time period, T₀ = 0.5 s, initial temperature

T_i = 20° C and final temperature, T_f = 30°C

Expansion in length, Δl = l α (T_f - T_i)

⇒ Δl = l × 9 × 10^-7 (30 - 20)

Now, the time period of pendulum,

T = `2pisqrt(l/"g")`

Error In time period,

`(Delta"t")/"T" = 1/2 (Delta"l")/"l" + 1/2 (Delta"g")/"g"`

Since, Δg = 0

`(Delta"T")/"T" = 1/2 (Delta "l")/"l"`

Now, substituting values in the above equation, we get,

`=> (Delta "T")/0.5 = 1/2 [(l xx 9 xx 10^-7)/l (30 - 20)]`

`=> Delta "T" = (0.5 xx 9 xx 10^-7 xx 10)/2`

`=> Delta "T" = 2.25 xx 10^-6`s