Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given:
Cross-sectional area of steel rod A = 4 cm2 = 4 × 10−4 m2
Length of steel rod L = 2 m
Compression during night hours ΔL = 0.1 cm = 10−3 m
Young modulus of steel Y = 1.9 × 1011 N m−2
Let the tension developed at night be F.
\[Y = \frac{F}{A} \times \frac{L}{∆ L}\]
\[ \Rightarrow F = \frac{YA ∆ L}{L}\]
\[ = \frac{1 . 9 \times {10}^{11} \times 4 \times {10}^{- 4} \times {10}^{- 3}}{2}\]
\[ = 3 . 8 \times {10}^4 N\]
∴ Required tension developed in steel rod during night hours = 3.8 × 104 N.
APPEARS IN
RELATED QUESTIONS
Two wires of diameter 0.25 cm, one made of steel and the other made of brass are loaded as shown in Fig. 9.13. The unloaded length of steel wire is 1.5 m and that of brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.
Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 cm and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.
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
A wire elongates by 1.0 mm when a load W is hung from it. If this wire goes over a a pulley and two weights W each are hung at the two ends, he elongation of he wire will be
Young's modulus of a perfectly rigid body is ______.
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
The temperature of a wire is doubled. The Young’s modulus of elasticity ______.
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 ______.
Identical springs of steel and copper are equally stretched. On which, more work will have to be done?
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?
A steel rod of length 2l, cross sectional area A and mass M is set rotating in a horizontal plane about an axis passing through the centre. If Y is the Young’s modulus for steel, find the extension in the length of the rod. (Assume the rod is uniform.)
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.
If Y, K and η are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.
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 ______.
The force required to stretch a wire of cross section 1 cm2 to double its length will be ______.
(Given Young's modulus of the wire = 2 × 1011 N/m2)
Young's modulus is also known as ______.
