Question

On increasing the length of a second's pendulum by Z%, its time period will

• A. increase by 2 Z%
• B. decrease by Z%
• C. decrease by 2 Z%
• D. increase by 0.5 Z%

Answer 1

Answer: (D)

increase by 0.5 Z%

New length, $L^{\prime }=L(1+Z/100)$
Since $T\propto \sqrt{L}$
Thus, $T^{\prime }=T\times \sqrt{1+Z/100}$
Thus, $\frac{T^{\prime }-T}{T}=\sqrt{1+Z/100}-1$
Assuming Z to be very small, using Binomial approximation, $(1+\frac{Z}{100}{)}^{1/2}=1+\frac{Z}{2\times 100}$
Thus, $\frac{T^{\prime }-T}{T}=1+0.5\frac{Z}{100}-1=0.5Z$ %