1.

Define Hooke's law of elasticity and describe an experiment to determine the Young's modulus of the material of wire.

Answer»

Solution :Hooke.s Law : Within elastic limit, stress is directly propportional to strain.
`therefore"strain"prop"stress"`
`("stress")/("strain")="CONSTANT"(E)`
where E constant called modulus of
elasticity of the material of a body.
Determination of young.s modulus of
a wire : The apparatus used to find young.s
modulus of a wireconsists of two long wires
A and B of same length made with same
material are used. These two wires are sus-
pended from a rigid support and a vernier
scale .V. is attached to them. Wire A is con-
nected to the main scale (M). A fixed load
is connected to this cord to keep tension
in the wire .This is called reference Wire. The
second wire. .B. is connected to vernier scale
.V.. Adjustable load hnger is connected to
this wire. This is called experimental wire.
Procedure : Let a load `M_(1)` is attached to
the weight HANGER at vernier. Main scale
reading (M.S. R) and vernier scale reading
(V.S.R) are NOTED. Weights are gradually
INCREASED in the steps of `(1)/(2)kg` upto a maxi-
mum load of say 3 kg . Every time M.S.R and
V.S.R are noted for every load, values are
posted in tabular form.
Let `1^(st)` reading with mass `M_(1)"is"e_(1)` and
`2^(nd)"reading with mass"M_(2)"is"e_(2).`
Change in load `M=M_(2)-M_(1)`
`"elongation"e=e_(2)-e_(1)`
.M. and .e. values are calculated and a garaph
is plotted.

Average `m//e=`
Force on the wire =mg
Area of cross section of the wire `pir^(2)`
`(r=radius of the wire)`
Elongation = e
Original length = l
`"Stress=((F)/(a))=(mg)/(pir^(2))`
`"Strain"=((e)/(l))`
`"Young.s modulus,"Y=(("stress")/("strain"))`
`thereforeY=((mg//l)/(epir^(2)))=((gl)/(pir^(2)))((m)/(e))`

A graph is between load (m) and
elongation .e., is straight line passing through
the origin. The SLOPE of the graph `(tantheta)`
gives `((m)/(e))`. This value is substituted in the
above eqution to find Young.s modulus of
the material of the wire.
Precations :
1. The load applied should be much smaller
than elastic limit.
2. Reading is noted only after the air bubble
is brought to centre of sporit level.


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