Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2019PhysicsMechanical Properties of SolidsActual

A steel wire of cross-sectional area 4 cm 2 has elastic limit of 2 . 2 × 10 8 N m - 2 . The maximum upward acceleration that can be given to a 1000 kg elevator supported by this steel wire if the stress is to exceed one-fourth of the elastic limit is [Take, g = 10 m s - 2 ]

Options

  1. A10   m   s - 2
  2. B9   m   s - 2
  3. C15   m   s - 2
  4. D12   m   s - 2

Correct answer

D. 12   m   s - 2

Step-by-step solution

Given, Y = 2 . 2 × 10 8   m   s - 2 Area of cross-section of steel wire, A = 4   cm 2 = 4 × 10 - 4   m 2 Mass of elevator, m = 1000   kg The maximum tension in the steel wire that can support elevator is given by T = 1 4 ×  stress  ×  area of cross-section  = 1 4 × 2 . 2 × 10 8 × 4 × 10 - 4 = 2 . 2 × 10 4   N   m - 2 If f be the maximum upward acceleration of the elevator, then T = m   g + f 2 . 2 × 10 4 =

Practice Mechanical Properties of Solids on Quantrex Academy →

More from Mechanical Properties of Solids

Two wires of the same material (Young's modulus =Y ) and same length L but radii R and 2 R respectively, are joined end to end and a weight w is suspended from the combination as s 2024With rise in temperature, the Young's modulus of elasticity: 2024Young's modules of materials of a wire of Length ' L ' and cross-sectional area A is Y . If the length of the wire is doubled and cross-sectional area is halved then Young's module 2024Young's moduli of the material of wires A and B are in the ratio of 1: 4 , while its area of cross sections are in the ratio of 1: 3 . If the same amount of load is applied to both 2023A 100 ~m long wire having cross-sectional area 6.25 10⁻⁴ ~m ^2 and Young's modulus is 10¹⁰ Nm ⁻² is subjected to a load of 250 ~N , then the elongation in the wire will be : 2023There are two wire of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by 2020A rubber cord has a cross-sectional area 10 - 6 m 2 and total unstretched length 0 . 1 m . It is stretched to 0 . 125 m and then released to project a particle of mass 5 . 0 g . Th 2019Breaking stress of a steel wire is p and the density of steel is ρ . The greatest length of steel wire that can hang vertically without breaking is 2018 Full Mechanical Properties of Solids list All BITSAT PYQs