Question

In a spring block system length of the spring is reduced by $1\%$, the time period will

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

Answer 1

Answer: (D)

decrease by $0.5\%$

$T=2\pi \sqrt{\frac{m}{k}}$
$T_1=2\pi \sqrt{\frac{l}{g}}$
$T_2=2\pi \sqrt{\frac{l(1-0.01)}{g}}$
$\Delta T=\frac{T1-T_2}{T_1}\times 100$
$=\frac{\sqrt{\frac{l}{g}}-\sqrt{\frac{l\left(0.99\right)}{g}}}{\sqrt{\frac{l}{g}}}\times 100$
$=0.501$
$\therefore 0.5\%$