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
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 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.
When some wax is rubbed on a cloth, it becomes waterproof. Explain.
A rope 1 cm in diameter breaks if the tension in it exceeds 500 N. The maximum tension that may be given to a similar rope of diameter 2 cm is
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 load of 10 kg is suspended by a metal wire 3 m long and having a cross-sectional area 4 mm2. Find (a) the stress (b) the strain and (c) the elongation. Young modulus of the metal is 2.0 × 1011 N m−2.
Answer in one sentence.
Define strain.
Modulus of rigidity of ideal liquids is ______.
The maximum load a wire can withstand without breaking, when its length is reduced to half of its original length, will ______.
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?
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 ______.
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 ______.
The stress-strain graph of a material is shown in the figure. The region in which the material is elastic is ______.
Answer in one sentence:
What is an elastomer?
The SI unit of stress is ______.
When an elastic body is in equilibrium in its altered shape, the magnitude of the external deforming force is ______.
