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 Aim:To determine:

  acceleration due to gravity 'g' using compound pendulum.

  radius of gyration about an axis passing through its centre of gravity .

  moment of inertia about an axis perpendicular to the plane of oscillation and passing through the centre of gravity of compound pendulum.

Theory:

In the fig(1), O is the point of suspension, G is the centre of gravity and O' is the centre of oscillation.

OO' is the length l of an equivalent simple pendulum. The acceleration due to gravity 'g' at the place is

given by;

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

Where T is the period of oscillations of the pendulum about O.

figure(1)

If and radius of gyration is given by the expression , ....................(2)

Moment of inertia I of the pendulum about an axis passing through its centre of gravity, ....................(3)

Where M is the mass of the pendulum.

1.  The compound bar pendulum AB is suspended by passing the knife edge through first hole from the end A. The

pendulum is pulled aside through a small angle and released. The pendulum oscillates in a vertical plane with a small

amplitude. The time for 10 oscillations is calculated. From this the period(T) of the oscillation of the pendulum is

determined.

In a similar manner periods of oscillations are determined by suspending the pendulum through all the holes on the

side of the centre of gravity G of the bar.(The bar is then inverted and the period of oscillations are determined by

suspending the pendulum through all the holes on the other side of the centre of gravity G). The distances 'd ', of the

top edges of different holes from the end of the bar is measured for each case.

The distance of the centre of gravity of the bar from the end A is noted by balancing the bar horizontally on a knife

edge. The mass of the pendulum is also determined.

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To find the radius of gyration: 

Calculation:

Acceleration due to gravity , =.....m/sec2 

Mass of the pendulum=.....Kg

Radius of gyration =.....m

Moment of inertia =Mk2=.....Kgm2 

Results:(i)The acceleration due to gravity=......m/s2

(ii)Moment of inertia of the bar about an axis passing through the centre of gravity=.....Kgm2 

V

1)  The time taken by a pendulum to complete one oscillation is called its Time

periodAmplitude

FrequencyVelocity

2)  The maximum displacement of the compound pendulum from its mean position is called Time period Amplitude

Frequency Velocity

3)  The moment of momentum is called 

Sl.No h1=AD/2 h2=BC/2 k=(h1h2)

1/2 

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  torque moment of inertia

angular momentum linear momentum

4)  What is the rotational analog corresponds to mass in linear motion? Inertial mass Moment of inertia

Radius of gyration Torque

5)  Moment of inertia of a rectangular strip of length ‘l’ and breadth ‘b’ is given by (M/12)(l²+b²)² (M/2) (l²+b²)²

(M/2) (l²+b²) (M/12)(l²+b²)