Advertisements
Advertisements
प्रश्न
A rigid bar of mass M is supported symmetrically by three wires each of length l. Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to ______.
विकल्प
`Y_(copper)/Y_(iron)`
`sqrt((Y_(iron))/(Y_(copper)`
`Y_(iron)^2/Y_(copper)^2`
`Y_(iron)/Y_(copper)^2`
Advertisements
उत्तर
A rigid bar of mass M is supported symmetrically by three wires each of length l. Those at each end are of copper and the middle one is of iron. The ratio of their diameters, if each is to have the same tension, is equal to `underline(sqrt((Y_(iron))/(Y_(copper))`.
Explanation:
As the bar is supported symmetrically by the three wires, therefore extension in each wire is the same.
Let T be the tension in each wire and the diameter of the wire is D, then Young’s modulus is `Y = "Stress"/"Strain"`
= `(F/A)/((ΔL)/L)`
= `F/A xx L/(ΔL)`
= `F/(pi(D/2)^2) xx L/(ΔL)`
= `(4FL)/(piD^2ΔL)`
⇒ `D^2 = (4FL)/(piΔLY)`
⇒ `D = sqrt((4FL)/(piΔLY)`
As F and `L/(ΔL)` are constants.
Hence, `D ∝ sqrt(1/Y)`
or `D = K/sqrt(Y)` ......(K is the proportionality constant)
Now, we can find ratio as `D_(copper)/D_(iron) = sqrt(Y_(iron)/Y_(copper)`
APPEARS IN
संबंधित प्रश्न
The stress-strain graphs for materials A and B are shown in Figure
The graphs are drawn to the same scale.
(a) Which of the materials has the greater Young’s modulus?
(b) Which of the two is the stronger 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;
A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm2. Calculate the elongation of the wire when the mass is at the lowest point of its path.
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 steel rod of cross-sectional area 4 cm2 and 2 m shrinks by 0.1 cm as the temperature decreases in night. If the rod is clamped at both ends during the day hours, find the tension developed in it during night hours. Young modulus of steel = 1.9 × 1011 N m−2.
Young's modulus of a perfectly rigid body is ______.
Identical springs of steel and copper are equally stretched. On which, more work will have to be done?
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.)
If the yield strength of steel is 2.5 × 108 Nm–2, what is the maximum weight that can be hung at the lower end of the wire?
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.
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 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 ______.
What does the dimensional formula [L⁻¹M¹T⁻²] represent?
In the formula Y = MgL/(πr²l), what does 'l' represent?
