Procedure

Apparatus

Kater's pendulum, stopwatch, meter scale and knife edges.

Real Lab Procedure

• Shift the weight W1 to one end of katers pendulum and fix it. Fix the knife edge K1 just below it.
• Keep the knife edge K2 at the other end and fix the wooden weight W2 symmetrical to other end. Keep the small weight 'w' near to centre.
• Suspend the pendulum about the knife edge 1 and take the time for about 10 oscillations. Note down the time t1 using a stopwatch and calculate its time period using equation T1=t1/10.
• Now suspend about knife edge K2 by inverting the pendulum and note the time t2 for 10 oscillations. Calculate T2 also.
• If T2 not equal to T1, adjust the position of knife edge K2 so that T2 approximately equal to T1.
• Balance the pendulum on a sharp wedge and mark the position of its centre of gravity. Measure the distance of the knife-edge K1 as h1 and that of K2 as h2 from the centre of gravity.

Observations and Calculations

To determine T₁ and T₂

Distance of K1 from C.G,h1 = ...............m.

Distance of K2 from C.G,h2 =...............m.

$$g=\frac{8\pi^{2}}{\frac{T_{1}^{2}+T_{2}^{2}}{h_{1}+h_{2}}+\frac{T_{1}^{2}-T_{2}^{2}}{h_{1}-h_{2}}}$$

Acceleration due to gravity, g =...............ms^-2.

Simulation

• Choose desired environment from combo box.
• Select suitable values for mass of wood cylinder and mass of steel cylinder.
• Choose the position of knife edge, steel and wood cylinder by changing the sliders for it.
• After choosing values, place the mouse over wood cylinder, drag and make it to oscillate.
• Note the time for 10 oscillations, by clicking on the **START** and **STOP** button of the stop watch.
• Click on **STOP** button under variables, for the pendulum to stop oscillating.
• Click on the **Invert** button to invert the pendulum.
• Again take the time for 10 oscillations.
• Click on **Show Measurements** checkbox to get the value of h₁ and h₂.
• Repeat the experiment by changing the values in **variables**.

**Note**-When you click on the wood or steel cylinder after selecting all the variables, a box appears if the selected values is not applicable.

Result

The acceleration due to gravity at a given place is found to be =...............ms^-2.