Question

The time period of simple pendulum is $T$. If its length is increased by $2$ the new time period becomes

• A. $0\cdot 99T$
• B. $1\cdot 01T$
• C. $1\cdot 02T$
• D. $0\cdot 98T$

Answer 1

The correct option is B $1\cdot 01T$

As we know,
The time period of simple pendulum,
$T=2\pi \sqrt{\frac{L}{g}}$
If it's length is increased by two 2%
$T^{\prime }=2\pi \sqrt{\frac{L(1+2/100)}{g}}$
$\frac{T^{\prime }}{T}=(1+\frac{2}{100{)}^{\frac{1}{2}}}$
$=1+\frac{1}{2}\cdot \frac{2}{100}$
$=1\cdot 01$
$T^{\prime }=1\cdot 01T$
Final answer ; (d)