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A massive rod of length 1m is placed on a smooth horizontal surface is pulled longitudinally by a force of 10N as shown in figure.
The tension in rod varies as T=10√x.How will linear mass density vary with x?
Asked by mailkunalmunjal | 09 Sep, 2020, 06:19: AM
Expert Answer
Let a massive rod of 1 m length is subjected to a force 10 N as shown in figure. Let M be the mass of rod.
Acceleration a of whole rod = Force / mass = ( 10 / M )
let us consider a small mass element dm at a distance x and having width dx.
Tension forces acting at forward and backward direction are shown in figure .
Forward direction tension force , TF = 10
Backward direction tension force, TB = 10
By Newton's second law, TF - TB = dm × a
Hence we have , ................(1)
where λ is linear mass density.
After simplification , eqn.(1) can be written as
Hence , λ = ( M/2 ) ( 1 / √x )
Hence linear mass density λ ( 1 / √x )
Answered by Thiyagarajan K | 15 Oct, 2020, 11:47: PM
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