Question

A clock which has pendulum made of brass keeps correct time at ${30}^{\circ }\text{C}$. How many seconds it will lose or gain in a day if temperature falls to $0^{\circ }\text{C}$. $\left({\alpha }_{brass}=1.8\times {10}^{-3}{/}^{\circ }{\text{C}}^{-1}\right)$

• A. $23.33sec$
• B. $24.33sec$
• C. $26.33sec$
• D. $25.33sec$

Answer 1

The correct option is A $23.33sec$

$T_0=2\pi \sqrt{\frac{L_0}{g}}T+2\pi \sqrt{\frac{L}{g}}T=T_0(1+\frac{\alpha \Delta \theta }{2})T=30[1+(1.8\times {10}^{-3}\times \frac{30}{2}\left)\right]T=30[1+(0.9\times {10}^{-3}\times 30\left)\right]T=23.33sec$