Procedure

Apparatus

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

Real Lab Procedure

• Shift the weight W₁ to one end of Kater’s pendulum and fix it.
• Fix the knife edge K₁ just below W₁.
• Place the knife edge K₂ at the opposite end and fix the wooden weight W₂ symmetrically to balance the setup.
• Position the small weight w near the center of the rod.
• Suspend the pendulum about knife edge K₁ and record the time t₁ for 10 oscillations using a stopwatch.
• Calculate the time period using the equation: T₁ = t₁ / 10.
• Invert the pendulum and suspend it about knife edge K₂.
• Record the time t₂ for 10 oscillations and compute T₂ = t₂ / 10.
• If T₂ is not equal to T₁, adjust the position of knife edge K₂ so that T₂ approximately equals 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.