Question

describe koenig's method for determining young's modulus of the material of the beam​

Answer 1

Describe koenig's method for determining young's modulus of the material of the beam​

Answer:

Aim

To determine Young’s modulus of elasticity of the material of a given wire.

Apparatus  

Searle’s apparatus, two long steel wires of same length and diameter, a metre scale, a screw gauge, eight 1/2 kg slotted weights and a 1 kg hanger.

Theory  

If a wire of length L and radius r be loaded by a weight Mg and if l be the increase in length.

Procedure

• Take two steel wires of same length and diameter and tight their ends in torsion screws A, B and C, D as shown in diagram. Wire AB becomes experimental wire and wire CD becomes auxiliary wire.

• Suspend a 1 kg dead load from hook of frame F2.

• Suspend a 1 kg hanger and eight 1/2 kg slotted weights from hook of frame F1. The experimental wire becomes taut.

• Remove kinks from experimental wire by pressing the wire between nails of right hand thumb and first finger (through a handkerchief) and moving them along the length of the wire.

• Remove all slotted weights from hanger. Now each wire is equally loaded with 1 kg weight.

• Measure length of experimental wire from tip A to tip B using a metre scale.

• Find the pitch and the least count of the screw gauge.

• Measure diameter of the experimental wire at five different places, equally spaced

• along the length (near two ends, two quarter distance from ends and middle). At each place, measure diameter along two mutually perpendicular directions. Record the observations in the table.

• Note the breaking stress for steel from table of constants. Multiply that by the cross section area of the wire to find breaking load of the wire. The maximum load is not to exceed one-third of the breaking load.

• Find the pitch and the least count of the spherometer screw attached to frame F1.

• Adjust the spherometer screw such that the bubble in the spirit level is exactly in the centre. Note the reading of the spherometer disc. This reading is recorded against zero load.

• Gently slip a 1/2 kg slotted weight in the hanger and wait for two minutes to allow the wire to extend fully. Bubble moves up from the centre.

• Rotate the spherometer screw to bring the bubble back to centre. Note the reading of the spherometer disc. This reading is recorded against 1 kg load in load increasing column.

• Repeat steps 12 and 13 till all the eight 1/2 kg slotted weights have been used (now total load on experimental wire is 5 kg which must be one-third of the breaking load).

• Now remove one slotted weight (load decreasing), wait for two minutes to allow the wire to contract fully. Bubble moves down from the centre.

• Repeat step 13. The reading is recorded against load in hanger in load decreasing column.

• Repeat steps 15 and 16 till all the eight slotted weights are removed (now load on experimental wire is 1 kg the initial load).

• (Observations for same load in load increasing and in load decreasing column must not differ much. Their mean is taken to eliminate the error.)

Y=mgl/$\pi$r2L