Question

The acceleration due to gravity increases by 0.5

Answer 1

Complete Question:

"The acceleration due to gravity increase by 0.5% when we go from the equator to the poles. What Will be the time period of the pendulum at the equator which beats seconds at the poles?

A) 1.950s B) 1.995s C) 2.050s D) 2.005s"

Answer:

D) 2.005s

Explanation:

The acceleration due to gravity is increased by 0.5%.

$g'=g+0.005 g\\\\g'=1.005g$

We know that,

$T_1=2\pi\sqrt{\frac{l}{g} }$

Where l is the length of the pendulum, g is the acceleration due to gravity and T is the time period.

$T=2\pi\sqrt{\frac{l}{1.005g} } =\frac{1}{\sqrt{1.005} }\times 2\pi\sqrt{\frac{l}{g'} }$

We can substitute the value   $2\pi\sqrt{\frac{l}{g} }$ in the above equation,

$T_1=2\times 1.0024=2.005s$

Hence the required answer is 2.005 s.

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