Q.1: Define simple pendulum.
Ans. An ideal simple pendulum is defined as ‘single isolated particle suspended by a weightless,
flexible and inextensible string with a friction-less support’.
Q.2: Why the word ‘SIMPLE’ is used before the pendulum?
Ans. Because the pendulums used in the wall clocks are ‘COMPOUND PENDULUMS’, in which a metallic rod is used in place of the thread.
Q.3: Define ‘g’?
Ans. Acceleration due to gravity.
Q.4: What is the difference between ‘g’ and ‘G’?
Ans. The value of G (gravitational constant) remains constant throughout the universe, whereas the value of ‘g’ decreases with the increase in the height.
Q.5: What is the value of ‘g’ at the C.G. of the earth?
Q.6: How the value of ‘g’ changes as we move from the surface towards the C.G. of the earth?
Ans. As a rule it should decrease gradually but due to variable density of the earth, it increases up to a small depth and then decreases.
Q.7: Where the ‘g’ is greater, at equator or poles?
Ans. At the poles (where the earth is slightly compressed).
Q.8: Where ‘g’ will be smaller, at Karachi or at Muree?
Ans. At Muree (7000 ft. above sea level).
Q.9: What is the value of ‘g’ at sea level?
Ans. g = 9.781 m/s2 at equator.
g = 9.832 m/s2 at poles.
Q.10: Why the amplitude of the pendulum is kept small (2cm or about 5 cm)?
Ans. If the amplitude is large the motion of the simple pendulum will not be simple harmonic. If θ will not be small Sinθ ≠ θ and T ≠ 2 √L/g.
Q.11: Define simple harmonic motion (S.H.M).
Ans. The motion of the vibrating body is S.H.M. when
(a) The magnitude of its acceleration is directly proportional to the displacement x from the mean position.
(b) The direction of acceleration is always towards the mean position (that is opposite to x) mathematically: a α – x
Q.12: Define vibratory system?
Ans. Back and forth or to and from motion between two fixed positions.
Q.13: Define the following terms: (a) amplitude (xo) (b) oscillation or vibration (c) frequency (f) (d) time period (T)
Ans. (a) Amplitude: the maximum displacement from the mean (equilibrium) position.
(b) Oscillation: the motion from one extreme position to the other and then back to the original one.
(c) Frequency: number of vibrations per second.
(d) time period: time taken for one vibration.
Q.14: What is the relation between frequency and time period?
Ans. f = (1 / T) or T = (1/F)
Q.15: What are the units of frequency?
Ans. Vibrations / sec, cycles / sec (c.p.s.) or Hertz.
Q.16: What is the frequency of a second pendulum?
Ans. 0.5 Hz or (1 / 2) Hz, because f = ( 1 / T ) = (1 / 2) ( T = 2 s for a second’s pendulum)
Q.17: Prove that g = 4 π2 (L / T2)
Ans. For a simple pendulum time period is given by:
T = 2 π √L/g
T2 = 4 π2 L/g
i.e. g = 4 π2 L/T2
Where L = length of the simple pendulum.
Q.18: Let the time period of a simple pendulum is 4s at the place where g = 900 cm/s2. What will be the time period at the place where g = 100 cm/s2.
Ans. 12 s.
EXPLANATION: g = 4 π2 (L/T2) => T2 α ( 1 / G) when L remain constant. Therefore, when g decreases by 9 times, the ‘T’ increases by 3 times.
Q.19: Time period will increase or decrease if we use a heavier bob.
Ans. There will be no change in the time period. EXPLANATION: The relation T = 2 √L/g shows that there is no effect of mass on the
Q.20: Can you replace the thread by a metallic wire?
Ans. No, because the wire is not flexible. EXPLANATION: By definition of simple pendulum, the string must be perfectly flexible. The
thread is flexible but a metallic wire is not. That is why the wire can be used in place of thread.
Q.21: What is restoring force?
Ans. The force which tends to bring a vibrating body towards the mean position.
Q.22: What is restoring force (net force) acting on the bob?
Ans. If the air friction is neglected, restoring force on the bob = mg Sin θ.
Q.23: What is net force on the bob, at equilibrium (mean) position?
Ans. Zero, since at mean position the weight of the bob is perfectly balanced by the tension (T) in the string.
Q.24: Define equilibrium.
Ans. A body is said to be in equilibrium when its linear and angular accelerations are zero or when F = 0 &
EXPLANATION: when a body is
(a) at rest or
(b) moving with uniform linear velocity its linear acceleration is zero.
(c) not rotating at all or
(d) rotating at a constant rate it is in equilibrium.
Q.25: Can you replace the thread by a rubber band?
Ans. No, because it is not inextensible. By definition the string must be inextensible.
Q.26: Can we use a cricket ball in place of the bob?
Ans. No, by definition of simple pendulum the bob must be as small as possible.
Q.27: Why the pendulum stops after some time?
Ans. Its energy is lost as heat.
Q.28: How P.E. and K.E. of the pendulum interchange into each other during vibrations?
Ans. (a) In the form of P.E. at extreme positions.
(b) In the form of K.E. at mean position and
(c) In the form of P.E. and K.E. between mean and extreme positions.
Q.29: From where the length of the pendulum is measured?
Ans. From the centre of gravity of the bob to the point of suspension.