Question

A pendulum clock loses $12s$ a day if the temperature is ${40}^{\circ }C$ and goes fast by $4s$ a day if the temperature is ${20}^{\circ }C$. Find the temperature at which the clock will show correct time.

• A. $T={25}^{\circ }C$
• B. $T={15}^{\circ }C$
• C. $T={20}^{\circ }C$
• D. $T={27.5}^{\circ }C$

Answer 1

The correct option is A $T={25}^{\circ }C$

Let $T$ be the temperature at which the clock is correct.

Time lost per day$=\frac{1}{2}\alpha$ (rise in temperature) $\times 86400$
$⟹12=\frac{1}{2}\alpha (40-T)\times 86400$ (i)
Time gained per day $=\frac{1}{2}\alpha$ (drop in temperature) $\times 86400$
$⟹4=\frac{1}{2}\alpha (T-20)\times 86400$ (ii)
Dividing equation (i) by equation (ii), we get
$12(T-20)=4(40-T)⟹T={25}^{\circ }C$
$⟹$ Clock shows correct time at ${25}^{\circ }C$