What is the period of the pendulum?

Question

1) A bob of mass 120 g is hanging from a string of length 25 cm. What is the period of the pendulum?
2) If you wanted to double period of the pendulum, what should you do?
A) Quadruple the length of the string.
B) Double the length of the string.
C) Double the mass.
D) Halve the length of the string.
3) Consider the equation for the period of a pendulum. In a plot of T2 vs. l you will get a straight line. The slope of the line is given by
A) 4pi2/g
B) g1/2
C) 2pig1/2
D) 2pi/g
4-) All clocks used to keep time by the swinging of a pendulum which had a period of 1 second. If one of these clocks were taken to the moon, how would the time kept by the clock change?
A) The moon clock would run slower than the earth clock.
B) The moon clock would run faster than the earth clock.
C) It would depend on spring constant of the pendulum.
D) The moon clock would keep the same time as the earth clock.

Answer 1

The time period of a simple pendulum =T = 2 pi * sq rt ( length / acceleration of gravity )

T = 2 pi sq rt ( l / g )

T = 1.0035 s
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2) time period T does not depend on mass of pendulum.

T is proportional to sq rt of length 'L'

Length L is proportional to square of time period T

when T is doubled ,L is quadrupled

hence A is the correct answer
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3) T^2=L*[ 4(pi)^2/g ]

The coefficient of L,that is [ 4(pi)^2/g ] is slope of T^2 vs L graph

hence A) is correct, The slope of the line is given by
A) 4pi2/g
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4) The acceleration of gravity of moon is 1/5 of acceleration of gravity of earth

T is inversely proportional to sq rt of 'g'

If 'g' is less , T will be more, block will go slow on moon

A) is correct
The moon clock would run slower than the earth clock.
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Answer 2

Pendulum motion is described by the equation
Period = 2 pi * sqrt ( length / acceleration of gravity ) or
T = 2 pi sqrt ( l / g )

(1) Plug in 25 cm and g in cm/s^2. The mass is irrelevant.
(2) The length is under the square root. How would you change the length to double the period?
(3) What's the slope of the line described by T ^ 2 = (2 pi ) ^ 2 * l / g?
(4) Gravity on the moon is 1/6 that of Earth. If you reduce g in the equation above, what happens to T?