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NEET-XII-Physics

14: Some Mechanical Properties of Matter

with Solutions - page 5
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  • #2
    A vertical metal cylinder of radius 2 cm and length 2 m is fixed at the lower end and a load of 100 kg is put on it. Find (a) the stress (b) the strain and (c) the compression of the cylinder. Young modulus of the metal = 2 × 1011 N m-2.
    Ans : Given:
    Radius of cylinder (r) = 2 cm = `` 2\times {10}^{-2}\,\mathrm{\,m\,}``
    Length of cylinder (L) = 2 m
    Mass of the load = 100 kg
    Young's modulus of the metal = `` 2\times {10}^{11}\,\mathrm{\,N\,}/{\,\mathrm{\,m\,}}^{2}`` (a) Stress(ρ) is given by: `` \frac{F}{A}``
    Here, F is the force given by mg = `` 100\times 10=1000\,\mathrm{\,N\,}`` ( Taking g = 10 m/s2)
    A is the area of cross-section = πr2 = 4π`` \times {10}^{-4}{\,\mathrm{\,m\,}}^{2}``
    `` \Rightarrow S\,\mathrm{\,tress\,}\rho =\frac{mg}{A}``
    `` =\frac{\left(100\times 10\right)}{\left(4\,\mathrm{\,\pi \,}\times {10}^{-4}\right)}``
    `` =7.96\times {10}^{5}\,\mathrm{\,N\,}/{\,\mathrm{\,m\,}}^{2}`` (b) Strain is given by:
    `` \,\mathrm{\,Strain\,}=\frac{\rho }{Y}=\frac{\left(7.96\times {10}^{5}\right)}{\left(2\times {10}^{11}\right)}``
    `` =4\times {10}^{-6}`` (c) Compression of the cylinder:
    ΔL = strain × L
    = 4 × 10-6 × 2 = 8 × 10-6 m
    Page No 300:
  • #2-a
    the stress
    Ans : Stress(ρ) is given by: `` \frac{F}{A}``
    Here, F is the force given by mg = `` 100\times 10=1000\,\mathrm{\,N\,}`` ( Taking g = 10 m/s2)
    A is the area of cross-section = πr2 = 4π`` \times {10}^{-4}{\,\mathrm{\,m\,}}^{2}``
    `` \Rightarrow S\,\mathrm{\,tress\,}\rho =\frac{mg}{A}``
    `` =\frac{\left(100\times 10\right)}{\left(4\,\mathrm{\,\pi \,}\times {10}^{-4}\right)}``
    `` =7.96\times {10}^{5}\,\mathrm{\,N\,}/{\,\mathrm{\,m\,}}^{2}``
  • #2-b
    the strain and
    Ans : Strain is given by:
    `` \,\mathrm{\,Strain\,}=\frac{\rho }{Y}=\frac{\left(7.96\times {10}^{5}\right)}{\left(2\times {10}^{11}\right)}``
    `` =4\times {10}^{-6}``
  • #2-c
    the compression of the cylinder. Young modulus of the metal = 2 × 1011 N m-2.
    Ans : Compression of the cylinder:
    ΔL = strain × L
    = 4 × 10-6 × 2 = 8 × 10-6 m
    Page No 300: