Advertisements
Advertisements
प्रश्न
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
पर्याय
500 N
250 N
1000 N
2000 N
उत्तर
\[F_1 = 500\text{N}\]
\[\text{ Let the required breaking force on the 2 cm wire be F .} \]
\[\text{ Breaking stress in 1 cm wire }= \frac{F_1}{A_1} = \frac{500}{\pi \left( \frac{0 . 01}{2} \right)^2}\]
\[\text{ Breaking stress in 2 cm wire }= \frac{F_2}{A_2} = \frac{F_2}{\pi \left( \frac{0 . 02}{2} \right)^2}\]
\[\text{ The breaking stress is the same for a material }. \]
\[ \Rightarrow \frac{500}{\pi \left( \frac{0 . 01}{2} \right)^2} = \frac{F_2}{\pi \left( \frac{0 . 02}{2} \right)^2}\]
\[ = > F_2 = 2000\text{N}\]
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.
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 ?
The yield point of a typical solid is about 1%. Suppose you are lying horizontally and two persons are pulling your hands and two persons are pulling your legs along your own length. How much will be the increase in your length if the strain is 1% ? Do you think your yield point is 1% or much less than that?
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 a metal wire is stretched by a load, the fractional change in its volume ∆V/V is proportional to
Answer in one sentence.
Define strain.
Answer in one sentence.
How should be a force applied on a body to produce shearing stress?
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 ______.
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 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.
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 ______.
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?
The stress-strain graph of a material is shown in the figure. The region in which the material is elastic is ______.
