A clock regulated by a seconds pendulum keeps correct time. During summer the length of the pendulum increases to 1.02m. How much will the clock gain or lose in one day ? 
 

The seconds pendulum,  time period $=\mathrm{T}=2\sec$

length of the second's pendulum $\mathrm{L}=\frac{{\mathrm{gT}}^2}{4{\mathrm{\pi }}^2}=0.9927\mathrm{m}$

length of seconds pendulum during the summer is = $1.02\mathrm{m}$

Now the error in length is.

$∆\mathrm{l}={\mathrm{l}}_2-{\mathrm{l}}_1=1.02-1=0.0273$

In the pendulum $T\propto \sqrt{l}$

By the principle of error,

$\frac{∆\mathrm{T}}{\mathrm{T}}=\frac{1}{2}\frac{∆\mathrm{l}}{\mathrm{l}}=\frac{1}{2}\frac{0.0273}{0.9927}=1188\sec .$

Hence the correct answer is 1188 sec.