By what factor should the length of a simple pendulum be changed in order to triple the period of vibration?
a. 3
c. 9
b. 6
d. 27

The length of the simple pendulum increased by a factor of 9.

Explanation:

The time period of vibration of a simple pendulum is given by :

.........(1)

l is the length of the simple pendulum

g is the acceleration due to gravity

If the time period of the simple pendulum is tripled, T' = 3 T

The new time period is given by :

..........(2)

Dividing equation (1) and (2) we get :

So, the length of the simple pendulum increased by a factor of 9. Hence, the correct option is (c) "9".

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it