Question

After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cm. She finds the pendulum makes 100 complete swings in a time of 145s.what is the value of g on this planet?g= ______ m/s^2?

Answer 1

Answer:

Acceleration due to gravity will be $g=5.718m/sec^2$

Explanation:

We have given length of pendulum l = 55 cm = 0.55 m

It is given that pendulum completed 100 swings in 145 sec

So time taken by pendulum for 1 swing $=\frac{145}{100}=1.45sec$

We have to find the acceleration due to gravity at that point

We know that time period of pendulum;um is given by

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

So $1.45=2\times 3.14\times \sqrt{\frac{0.55}{g}}$

$\sqrt{\frac{0.55}{g}}=0.230$

Squaring both side

${\frac{0.3025}{g}}=0.0529$

$g=5.718m/sec^2$

So acceleration due to gravity will be $g=5.718m/sec^2$

Answer 2

The value of g on this planet will be "10.317 m/s²".

According to the question,

Length of pendulum,

• L = 55 cm

Time per 100 swings,

• 145 s

Time per 1 swing,

• T = 1.45 s

By using the formula, we get

→ $g = 4\times \pi {\frac{L}{T^2} }$

By substituting the values, we get

→    $= 4\times (3.14)^2 {\frac{55}{(1.45)^2} }$

→    $= 1031.7 \ cm/S^2$

or,

→    $= 10.317 \ m/s^2$

Thus the above response is correct.

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