A clock which keeps correct time at 20° C, is subjected to 40° C . If coefficient of linear expansion of the pendulum is 12 × 10-6 / ° C. How much will it gain or lose time ?

Question

A clock which keeps correct time at 20° C, is subjected to 40° C . If coefficient of linear expansion of the pendulum is 12 × 10-6 / ° C. How much will it gain or lose time ? (A) 10.3 s/day (B) 20.6 s/day (C) 5 s/day (D) 20 min/day

Tardigrade Admin · Accepted Answer

T=2 π √(I/g) (Δ T/T)= (1/2) (Δ l/l) =(1/2) α Δ θ =(1/2) × 62 × 10-6(40-20) =12 × 10-5 Δ T=T × 12 × 10-5 =24 × 60 × 60 × 12 × 10-5 =10.3 s / day

Q. A clock which keeps correct time at $2 0^{\circ} C$ , is subjected to $4 0^{\circ} C .$ If coefficient of linear expansion of the pendulum is $12 \times 1 0^{- 6} /^{\circ} C$ . How much will it gain or lose time ?

10.3 s/day

20.6 s/day

5 s/day

20 min/day

$T = 2 π \frac{I}{g}$
$\frac{Δ T}{T} = \frac{1}{2} \frac{Δ l}{l}$
$= \frac{1}{2} α Δ θ$
$= \frac{1}{2} \times 62 \times 1 0^{- 6} (40 - 20)$
$= 12 \times 1 0^{- 5}$
$Δ T = T \times 12 \times 1 0^{- 5}$
$= 24 \times 60 \times 60 \times 12 \times 1 0^{- 5}$
$= 10.3 s / d a y$

Q. A clock which keeps correct time at 20∘C, is subjected to 40∘C. If coefficient of linear expansion of the pendulum is 12×10−6/∘C. How much will it gain or lose time ?