a simple pendulum has a period of 3.45 seconds. when the length of the pendulum is shortened by 1.0m, the period is 2.81seconds. calculate the 1 , original length of the pendulum 2. value of the acceleration due to gravity?

VTPETERS2002

5 years ago

Answer
5.0/


Original length = 2.97 m

Explanation:

Let the original length of the pendulum be 'L' m

Given:

Acceleration due to gravity (g) = 9.8 m/s²

Original time period of the pendulum (T) = 3.45 s

Now, the length is shortened by 1.0 m. So, the new length is 1 m less than the original length.

New length of the pendulum is,

New time period of the pendulum is,

We know that, the time period of a simple pendulum of length 'L' is given as:

-------------- (1)

So, for the new length, the time period is given as:

------------ (2)

Squaring both the equations and then dividing them, we get:



Now, plug in the given values and calculate 'L'. This gives,



Therefore, the original length of the simple pendulum is 2.97 m

Jerrycurl12

5 years ago

T is directly proportional to the square root of l
hence

T1/√l1=T2/√l2

3.45/√1=2.81/√l2

3.45√l2=2.81
√l2=0.81

l2=(0.81)²

=0.66cm

T=√l/g

2.81²=l/g

7.9g=0.66

g=0.084ms^-2