Question

A pendulum of length 25 cm has a period of 1 s in a certain place. What is the value of g there? If the length of the pendulum is increased 5 ×, what would be the new time period?

a) ( g = 9.8 , m/s^2 ); ( T_new = 2 , s )

b) ( g = 5 , m/s^2 ); ( T_new = 5 , s )

c) ( g = 3.92 , m/s^2 ); ( T_new = 2.24 , s )

d) ( g = 2 , m/s^2 ); ( T_new = 10 , s )

Answer 1

The value of g is approximately 98π² m/s² in the given place. When the length of the pendulum is increased by 5, the new time period is approximately 2.24 s.

Step-by-step explanation:

The value of g can be calculated using the formula:

T = 2π√(L/g)

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

Given that the length of the pendulum is 25 cm and the period is 1 s, we can rearrange the formula to solve for g:

g = (4π²L) / T²

Substituting the values, we get:

g = (4π² * 25) / (1)² = 98π² m/s²

Therefore, the value of g in this place is approximately 98π² m/s².

When the length of the pendulum is multiplied by 5, the new length becomes 25 cm × 5 = 125 cm. To find the new time period, we can use the formula:

T_new = 2π√(L_new/g)

Substituting the values, we get:

T_new = 2π√(125/98π²) = 2√(125/98π)

Calculating this expression, we find that T_new ≈ 2.24 s.

Therefore, the correct answer is (c) ( g = 3.92 m/s² ); ( T_new = 2.24 s ).