Question

to determine the value of 'g' by using of bar pendulum

Answer 1

A bar pendulum with holes for hanging, Wall support for hanging, stop clock, meter scale, knife edge for measuring the center of mass of the bar. Purpose of experiment: To measure the acceleration due to gravity (g) by small oscillations of a bar pendulum. Theory The period of oscillations T of a body constrained to rotate about a horizontal axis for small amplitudes is given by the expression 212°°±²³³´µ=mgdITπ(1) where m is mass of the body , d is the distance between center of mass (CM) and the axis of rotation and Iis the moment of inertia ( MI) about the axis of rotation given by (from parallel axis theorem) 20mdII+=(2) where, Iois the moment of inertia about parallel axis through center of mass . If kis the radius of gyration ( i.e. I0= mk2). Then from eqs (1) and (2) ()22224dkgdT+=π(3) By recording the period of oscillations Tas a function dwe can determine the values of gravitational acceleration g as well as moment of inertia Io of the body . The plot of T Vs d , shows a minimum time period at d= K,given by 21min22°°±²³³´µ=gkTπ(4) Experimental Set-Up In this experiment the rigid body consists of a rectangular mild steel bar with a series of holesdrilled at regular interval to facilitate the suspension at various points along its length (see Fig.1). The steel bar can be made to rest on screw type knife-edge fixed on the wall to ensure the oscillations in a vertical plane freely. The oscillations can be monitored accurately using a telescope. The radius of gyration for this bar is