First slide

Thermal expansion

Question

A clock with a metallic pendulum is 5 seconds fast each day at a temperature of $15^{\circ} c$ and 10 seconds slow each day at a temperature of $30^{\circ} c$ , find the coefficient of linear expansion of the metal?

Moderate

A

$2.31 \times {10^{- 5}}^{\circ} c^{-1}$
B

$2.03 \times {10^{- 5}}^{\circ} c^{-1}$
C

$1.03 \times 10^{- 6} {}^{0}C^{- 1}$
D

$1.03 \times 10^{- 5} {}^{0}C^{- 1}$

Solution

Graduation temperature= $T_{o}$
change in time due to coefficient of linear expansion of material of pendulum is
$∆ t i m e = \frac{1}{2} α (t e m p e r a t u r e d i f f e r e n c e) x 86400 h e r e α i s c o e f f i c i e n t o f l i n e a r e x p a n s i o n o f m e t a l o f p e n d u l u m$
$5= \frac{1}{2} .α. (T_{o} -15) ×86400$ ----(1)
$10= \frac{1}{2} .α. ({30-T}_{o}) ×86400$ ----(2)
$o n d i v i d i n g e q n (1) w i t h e q n (2) \frac{1}{2} = \frac{T_{0} - 15}{30 - T_{0}} \Rightarrow T_{0} = 20^{0} C s u b s t i t u t e T_{0} v a l l u e i n e q n (1) 5 = \frac{1}{2} α (20 - 15) 86400 \Rightarrow α = 2.31 x 10^{- 5} {}^{0}C^{- 1} = c o e f f i c i e n t o f l i n e a r e x p a n s i o n o f m e t a l$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App