 Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
`        A Second’s pendulum gives correct time at 25C The pendulum shaft is thin and is made up of steel.How many seconds will it lose per day at 35C??(coeff. of linear expansion of steel = 11×10-5/C)`
one year ago

```							Dear student The period of a pendulum is: T = 2*π*sqrt( L/g ) With thermal expansion, the period will be longer. Let L = L*(1 + Δ) be the pendulum length at 35C. The longer period is: T2 = 2*π*sqrt( L*(1 + Δ) /g ) The correct number of periods counted per day is: N = 60*60*24 / ( 2*π*sqrt( L/g ) ) = 86400 / ( 2*π*sqrt( L/g ) ) The clock would count the same number of periods at 35C, but the time taken would be: t2 = N*2*π*sqrt( L*(1 + Δ) /g ) t2 = 86400 *2*π*sqrt( L*(1 + Δ) /g ) / ( 2*π*sqrt( L/g ) ) A lot of stuff cancels, and: t2 = 86400 * sqrt( 1 + Δ ) At the end of counting N periods at 35C, the clock has taken an amount of time greater than one day by: t2 - 86400 = 86400* ( sqrt(1 + Δ ) - 1) For brass, the thermal coefficient of expansion is α = 19*10^-6 C^-1. The length of a pendulum at 35C would be: ΔL = L1*α*ΔT = L * 19*10^-6 * 10 = L * 19*10-5 L2 = L + ΔL = L * ( 1 + α*ΔT ) In the above derivation, this was expressed as: L = L*( 1 + Δ ) Δ = 19*10^-5 So, the time error after N periods (one day) would be: Δt = 86400* ( sqrt(1 + Δ ) - 1) = 86400*( sqrt( 1 + 19*10^-5 ) - 1 ) = 8.2 sec
```
one year ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Thermal Physics

View all Questions »  ### Course Features

• 101 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions