Advertisements
Advertisements
Question
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
Options
500 N
250 N
1000 N
2000 N
Advertisements
Solution
\[F_1 = 500\text{N}\]
\[\text{ Let the required breaking force on the 2 cm wire be F .} \]
\[\text{ Breaking stress in 1 cm wire }= \frac{F_1}{A_1} = \frac{500}{\pi \left( \frac{0 . 01}{2} \right)^2}\]
\[\text{ Breaking stress in 2 cm wire }= \frac{F_2}{A_2} = \frac{F_2}{\pi \left( \frac{0 . 02}{2} \right)^2}\]
\[\text{ The breaking stress is the same for a material }. \]
\[ \Rightarrow \frac{500}{\pi \left( \frac{0 . 01}{2} \right)^2} = \frac{F_2}{\pi \left( \frac{0 . 02}{2} \right)^2}\]
\[ = > F_2 = 2000\text{N}\]
APPEARS IN
RELATED QUESTIONS
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.
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 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.
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.
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 some wax is rubbed on a cloth, it becomes waterproof. Explain.
The breaking stress of a wire depends on
When a metal wire is stretched by a load, the fractional change in its volume ∆V/V is proportional to
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 ______.
A mild steel wire of length 2L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (Figure). A mass m is suspended from the mid point of the wire. Strain in the wire is ______.
Is stress a vector quantity?
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 ______.
Answer in one sentence:
What is an elastomer?
The SI unit of stress is ______.
