Question

A clock with an Iron Pendulum keeps correct time at 20⁰C. How much will it lose or gain if temperature changes to 40ŗC? [Given cubical expansion of iron = 36 × 10^–6 ŗC^–1]

• A. 10.368 sec gain
• B. 10.368 sec loss
• C. 5.184 sec gain
• D. 5.184 sec loss

Answer 1

Answer: (B)

10.368 sec loss

Answer 2

T = 2p $\sqrt { \frac { \mathrm { L } } { \mathrm { g } } }$

and T¢ = 2p

or $\frac { T ^ { \prime } } { \mathrm { T } }$ =$\sqrt { \frac { \mathrm { L } ^ { \prime } } { \mathrm { L } } }$

L¢ = L(1 × a Dt)

\ a =$\frac { 36 \times 10 ^ { - 6 } } { 3 }$

= L(1 + 12 × 10^–6 × 20) = 12 × 10^–6 ŗC^–1

L¢ = L(1.00024)

$\frac { T ^ { \prime } } { \mathrm { T } }$ =$\sqrt { \frac { 1.00024 \mathrm {~L} } { \mathrm {~L} } }$

or = 1.00012

(Q T = 2 sec)

T¢ = 2.00024

Loss in time per day =$\frac { ( 2.00024 - 2 ) \times 24 \times 60 \times 60 } { 2 }$sec.

= 10.368 sec. Loss/day