Advertisements
Advertisements
प्रश्न
A rod of length l and negligible mass is suspended at its two ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths (Figure). The cross-sectional areas of wires A and B are 1.0 mm2 and 2.0 mm2, respectively.
(YAl = 70 × 109 Nm−2 and Ysteel = 200 × 109 Nm–2)
- Mass m should be suspended close to wire A to have equal stresses in both the wires.
- Mass m should be suspended close to B to have equal stresses in both the wires.
- Mass m should be suspended at the middle of the wires to have equal stresses in both the wires.
- Mass m should be suspended close to wire A to have equal strain in both wires.
Advertisements
उत्तर
b and d
Explanation:
Let the mass is placed at x from the end B.
Let TA and TB be the tensions in wire A and wire B respectively.
For the rotational equilibrium of the system,
∑τ = 0 ......(Total torque = 0)
⇒ `T_Bx = T_A (l - x)` = 0
⇒ `T_B/T_A = (l - x)/x` ......(i)
Stress in wire `A = S_A = T_A/a_A`
Stress in wire `B = S_B = T_B/a_B`
Where aA and aB are cross-sectional areas of wire A and B respectively.
By question aB = 2aA
Now, for equal stress SA = SB
⇒ `T_A/a_A = T_B/a_B`
⇒ `T_B/T_A = a_B/a_A` = 2
⇒ `(l - x)/x` = 2
⇒ `l/x - 1` = 2
⇒ `x = l/3`
⇒ `l - x = l - l/3 = (2l)/3`
Hence, mass m should be placed closer to B.
For equal train, (strain)A = (strain)B
⇒ `(Y_A)/S_A = Y_B/S_B` ......(Where YA and YB are Young moduli)
⇒ `Y_(steel)/(T_A/a_A) = Y_(Al)/(T_B/a_B)`
⇒ `Y_(steel)/Y_(Al) = T_A/T_B xx a_B/a_A = (x/(l - x))((2a_A)/a_A)`
⇒ `(200 xx 10^9)/(70 xx 10^9) = (2x)/(l - x)`
⇒ `20/7 = (2x)/(l - x)`
⇒ `10/7 = x/(l - x)`
⇒ `10l - 10x = 7x`
⇒ `17x = 10l`
⇒ `x = (10l)/17`
`l - x = l - (10l)/17 = (7l)/17`
Hence, mass m should be placed closer to wire A.
APPEARS IN
संबंधित प्रश्न
Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 ×106 Pa.
A rod of length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in Figure. The cross-sectional areas of wires A and B are 1.0 mm2 and 2.0 mm2, respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stresses and (b) equal strains in both steel and aluminium wires.
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 the skeleton of an elephant and the skeleton of a mouse are prepared in the same size, the bones of the elephant are shown thicker than those of the mouse. Explain why the bones of an elephant are thicker than proportionate. The bones are expected to withstand the stress due to the weight of the animal.
A wire can sustain the weight of 20 kg before breaking. If the wire is cut into two equal parts, each part can sustain a weight of
A spiral spring is stretched by a weight. The strain will be:
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 ______.
A rectangular frame is to be suspended symmetrically by two strings of equal length on two supports (Figure). It can be done in one of the following three ways;
| (a) |  |
| (b) |  |
| (c) |  |
The tension in the strings will be ______.
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.
A wire is suspended from the ceiling and stretched under the action of a weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.
- Tensile stress at any cross section A of the wire is F/A.
- Tensile stress at any cross section is zero.
- Tensile stress at any cross section A of the wire is 2F/A.
- Tension at any cross section A of the wire is F.
Is stress a vector quantity?
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?
A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1πms-2, what will be the tensile stress that would be developed in the wire?
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 ______.
A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s-1) with which it can be rotated about its other end in the space station is (Breaking stress of wire = 4.8 × 107 Nm-2 and the area of cross-section of the wire = 10-2 cm2) is ______.
What is an elastomer?
Strain is defined as the ratio of:
The SI unit of stress is:
What are the dimensions of strain?
