Advertisements
Advertisements
प्रश्न
A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the same tension.
Advertisements
उत्तर १
The tension force acting on each wire is the same. Thus, the extension in each case is the same. Since the wires are of the same length, the strain will also be the same.
The relation for Young’s modulus is given as:
`Y = "Stress"/"Strain" = (F/A)/"Strain" = ((4F)/(pid^2))/"Strain"` .....(i)
Where,
F = Tension force
A = Area of cross-section
d = Diameter of the wire
It can be inferred from equation (i) that `Y prop 1/d^2`
Young’s modulus for iron, Y1 = 190 × 109 Pa
Diameter of the iron wire = d1
Young’s modulus for copper, Y2 = 120 × 109 Pa
Diameter of the copper wire = d2
Therefore, the ratio of their diameters is given as:
`d_2/d_1 = sqrt(Y_1/Y_2) = sqrt((190xx10^9)/(120xx10^9)) = sqrt(19/12) = 1:25:1`
उत्तर २
Since each wire is to have same tension, therefore, each wire has the same extension. Moreover, each wire has the same initial length.So, the strain is same for each wire.
Now, `Y = "Stress"/"Strain" = (F/((piD^2)/4))/"Strain"`
or `Y prop 1/D^2 => D prop 1/sqrtY`
`D_"copper"/(D_"iron") = sqrt((Y_""iron)/(Y_"copper")) = sqrt((190 xx 10^9)/(110 xx 10^9)) = sqrt(19/11) =1.314`
APPEARS IN
संबंधित प्रश्न
A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 N m–2, what is the maximum load the cable can support?
A mild steel wire of length 1.0 m and cross-sectional area 0.50 × 10–2 cm2 is stretched, well within its elastic limit, horizontally between two pillars. A mass of 100 g is suspended from the mid-point of the wire. Calculate the depression at the midpoint.
Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9 × 107 Pa? Assume that each rivet is to carry one-quarter of the load.
When a block a mass M is suspended by a long wire of length L, the elastic potential potential energy stored in the wire is `1/2` × stress × strain × volume. Show that it is equal to `1/2` Mgl, where l is the extension. The loss in gravitational potential energy of the mass earth system is Mgl. Where does the remaining `1/2` Mgl energy go ?
A steel blade placed gently on the surface of water floats on it. If the same blade is kept well inside the water, it sinks. Explain.
A spiral spring is stretched by a weight. The strain will be:
A rod has a radius of 100 mm and a length of 10 cm. A 100 N force compress along its length. Calculate the longitudinal stress developed in the rod.
Modulus of rigidity of ideal liquids is ______.
A spring is stretched by applying a load to its free end. The strain produced in the spring is ______.
Consider two cylindrical rods of identical dimensions, one of rubber and the other of steel. Both the rods are fixed rigidly at one end to the roof. A mass M is attached to each of the free ends at the centre of the rods.
Consider a long steel bar under a tensile stress due to forces F acting at the edges along the length of the bar (Figure). Consider a plane making an angle θ with the length. What are the tensile and shearing stresses on this plane
- For what angle is the tensile stress a maximum?
- For what angle is the shearing stress a maximum?
The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are l1 and l2 respectively. The actual length of the metal wire is ______.
If 'S' is stress and 'Y' is young's modulus of the material of a wire, the energy stored in the wire per unit volume is ______.
Answer in one sentence:
What is an elastomer?
What is the physical quantity defined as the internal restoring force per unit area of a body?
Strain is defined as the ratio of ______.
The SI unit of stress is ______.
