NEET Physics - New - Mechanical Properties of Solids

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Question - 1

A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L1 when mass M is suspended from its free end. The expression for Young's modulus is___

  • A \(\frac{m g L}{A\left(L_{1}-L\right)}\)
  • B \(\frac{m g L_{1}}{A L}\)
  • C \(\frac{M g\left(L_{1}-L\right)}{A L}\)
  • D \(\frac{M g L}{A L_{1}}\)

Question - 2

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is: \(\left(\mathrm{a}_{\mathrm{Cu}}=1.7 \times 10^{-5} \mathrm{~K}^{-1}\right.\) and \(\left.\mathrm{a}_{\mathrm{Al}}^{-2.2} \times 10^{-5} \mathrm{~K}^{-1}\right)\)____

  • A \(113.9 \mathrm{~cm}\)
  • B \(88 \mathrm{~cm}\)
  • C \(68 \mathrm{~cm}\)
  • D \(6.8 \mathrm{~cm}\)

Question - 3

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes L + I. The elastic potential energy stored in the extended wire is____

  • A \(\mathrm{mg} \mathrm{I}\)
  • B \(\frac{1}{2} \mathrm{mgl}\)
  • C \(\frac{1}{2} \mathrm{mgL}\)
  • D \(\mathrm{mgl}\)

Question - 4

The approximate depth of an ocean is 2700 m. The compressibility of water is \(45.4 \times 10^{-11} \mathrm{~Pa}^{-1}\) and density of water is \(10^{3} \mathrm{~kg} / \mathrm{m}^{3}\). What fractional compression of water will be obtained at the bottom of the ocean?

  • A \(1.0 \times 10^{-2}\)
  • B \(1.2 \times 10^{-2}\)
  • C \(1.4 \times 10^{-2}\)
  • D \(0.8 \times 10^{-2}\)

Question - 5

Copper of fixed volume ' V ' is drawn into wire of length ' T '. When this wire is subjected to a constant force ' P ', the extension produced in the wire is \(\mathrm{D} l^{\prime}\). Which of the following graphs is a straight line?

  • A \(\mathrm{D} l\) versus 1/l
  • B \(\mathrm{D} l\) versus l2
  • C \(\mathrm{D} l\) versus 1/l2
  • D \(\mathrm{D} l\) versus l

Question - 6

If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be______

  • A \(\frac{7 q}{(5 s p)}\)
  • B \(\frac{5 q}{\left(7 s p^{2}\right)}\)
  • C \(\frac{7 q}{\left(5 s p^{2}\right)}\)
  • D \(\frac{2 q}{(5 s p)}\)

Question - 7

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

  • A \(Length =100 \mathrm{~cm}, diameter =1 \mathrm{~mm}\)
  • B \(Length =200 \mathrm{~cm}, diameter =2 \mathrm{~mm}\)
  • C \(Length =300 \mathrm{~cm}, diameter =3 \mathrm{~mm}\)
  • D \(Length =50 \mathrm{~cm}, diameter =0.5 \mathrm{~mm}\)

Question - 8

The compressibility of water is \(4 \times 10^{-5}\) per unit atmospheric pressure. The decrease in volume of \(100 \mathrm{~cm}^{3}\) of water under a pressure of 100 atmosphere will be___

  • A \(0.4 \mathrm{~cm}^{3}\)
  • B \(1 \times 10^{-5} \mathrm{~cm}^{3}\)
  • C \(0.025 \mathrm{~cm}^{3}\)
  • D \(0.004 \mathrm{~cm}^{3}\)

Question - 9

When an elastic material with Young's modulus Y is subjected to stretching stress S, elastic energy stored per unit volume of the material is_____

  • A \( YS/2\)
  • B \(\mathrm{S}^{2} \mathrm{Y} / 2\)
  • C \(\mathrm{S}^{2} / 2 \mathrm{Y}\)
  • D \(\mathrm{S} / 2 \mathrm{Y}\)

Question - 10

Two wires A and B are of the same material. Their lengths are in the ratio 1: 2 and the diameter are in the ratio 2: 1. If they are pulled by the same force, then increase in length will be in the ratio____

  • A 2: 1
  • B 1: 4
  • C 1: 8
  • D 8: 1