Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainPhysicsMechanical Properties of Solids

A bar of mass m and length l is hanging from point A as shown in the figure. If the Young's modulus of elasticity of the bar is Y and area of cross-section of the wire is A , then the increase in its length due to its own weight will be

Options

  1. Am g L 2 A Y
  2. Bm g A 2 L Y
  3. Cm g 2 L A Y
  4. D2 L Y m g A

Correct answer

A. m g L 2 A Y

Step-by-step solution

Consider a small section d x of the bar at a distance x from B. The weight of the bar for a length x is, W = m g L x . Elongation in x will be d e = W A Y d x = m g L A Y d x ⋅ x . Total elongation of the bar can be obtained by integrating this expression for x = 0 t o x = L . ∴ Δ l = ∫ x = 0 x = L d e = m g L A Y ∫ 0 L x ⋅ d x ⇒ Δ l = m g L 2 A Y

Practice Mechanical Properties of Solids on Quantrex Academy →

More from Mechanical Properties of Solids

Figure represents the extension ( l ) of a wire of length 1 meter, suspended from the ceiling of the room at one end with a load W connected to the other end. If the cross-sectiona 2026A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is 4 10^8 N/m ^2 and its radius is 4 mm, then maximum acceleration the li 2026The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire A and wire B is 20/11 . When the joined wire is ke 2026A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is 600 10⁻⁶ m ^3 . The elastic potential energy stored in the wire in stretch 2026The Young's modulus of steel wire of radius r and length L is Y . If the radius r and length L of the wire are doubled then the value of Y 2026Two wires as shown in the figure below, made of steel and have breaking stress of 12 10^8 N/m ^2 . Area of cross-section of upper wire is 0.008 cm ^2 and of lower wire is 0.004 cm 2026A cube has side length 5 cm and modulus of rigidity 10^5 N/m ^2 . The displacement produced by a force of 10 N in the upper face of cube is _____ mm. 2026A metal string A is suspended from a rigid support and its free end is attached to a block of mass M . Second block having mass 2M is suspended at the bottom of the first block usi 2026 Full Mechanical Properties of Solids list All 99 Percentile Qs Bank for JEE Main PYQs