Advertisements
Advertisements
Question
The Young’s modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?
Advertisements
Solution
Here `Y = "stress"/"strain"`
According to question, longitudinal stress for rubber and steel are equal
So, `Y ∝ Stress`
`Y_(Steel)/Y_(Rub ber) = (Stress)_(Steel)/(Stress)_(Rub ber)`
∵ `Y_(Steel) > Y_(Rub ber)`
`Y_(Steel)/Y_A > 1`
`(Stress)_(Steel) > (Stress)_(Rub ber)`
APPEARS IN
RELATED QUESTIONS
The figure shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?
Read the following statements below carefully and state, with reasons, if it is true or false
The Young’s modulus of rubber is greater than that of steel;
Two wires A and B are made of same material. The wire A has a length l and diameter rwhile the wire B has a length 2l and diameter r/2. If the two wires are stretched by the same force, the elongation in A divided by the elongation in B is
The length of a metal wire is l1 when the tension in it T1 and is l2 when the tension is T2. The natural length of the wire is
A student plots a graph from his reading on the determination of Young modulus of a metal wire but forgets to put the labels. the quantities on X and Y-axes may be respectively
(a) weight hung and length increased
(b) stress applied and length increased
(c) stress applied and strain developed
(d) length increased and the weight hung.
A uniform rectangular block of mass of 50 kg is hung horizontally with the help of three wires A, B and C each of length and area of 2m and 10mm2 respectively as shown in the figure. The central wire is passing through the centre of gravity and is made of material of Young's modulus 7.5 x 1010 Nm−2 and the other two wires A and C symmetrically placed on either side of the wire B are of Young's modulus 1011 Nm−2 The tension in the wires A and B will be in the ratio of:
Young's modulus of a perfectly rigid body is ______.
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
What is the Young’s modulus for a perfect rigid body ?
A steel rod (Y = 2.0 × 1011 Nm–2; and α = 10–50 C–1) of length 1 m and area of cross-section 1 cm2 is heated from 0°C to 200°C, without being allowed to extend or bend. What is the tension produced in the rod?
A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has the cable stretched? (Young’s modulus for steel is 2 × 1011 Nm–2.)
A steel wire of mass µ per unit length with a circular cross section has a radius of 0.1 cm. The wire is of length 10 m when measured lying horizontal, and hangs from a hook on the wall. A mass of 25 kg is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains << longitudinal strains, find the extension in the length of the wire. The density of steel is 7860 kg m–3 (Young’s modules Y = 2 × 1011 Nm–2).
In nature, the failure of structural members usually result from large torque because of twisting or bending rather than due to tensile or compressive strains. This process of structural breakdown is called buckling and in cases of tall cylindrical structures like trees, the torque is caused by its own weight bending the structure. Thus the vertical through the centre of gravity does not fall within the base. The elastic torque caused because of this bending about the central axis of the tree is given by `(Ypir^4)/(4R) . Y` is the Young’s modulus, r is the radius of the trunk and R is the radius of curvature of the bent surface along the height of the tree containing the centre of gravity (the neutral surface). Estimate the critical height of a tree for a given radius of the trunk.
A metal wire of length L, area of cross section A and Young's modulus Y behaves as a spring of spring constant k given by:
A boy's catapult is made of rubber cord which is 42 cm long, with a 6 mm diameter of cross-section and negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms-1. Neglect the change in the area of the cross-section of the cord while stretched. Young's modulus of rubber is closest to ______.
Young's modulus is also known as ______.
What does the dimensional formula [L⁻¹M¹T⁻²] represent?
