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
Advertisements
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
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.
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.
The ratio stress/strain remain constant for small deformation of a metal wire. When the deformation is made larger, will this ratio increase or decrease?
The breaking stress of a wire depends on
A heave uniform rod is hanging vertically form a fixed support. It is stretched by its won weight. The diameter of the rod is
When a metal wire is stretched by a load, the fractional change in its volume ∆V/V is proportional to
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 ______.
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 ______.
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 area of the cross-section of the rope used to lift a load by a crane is 2.5 × 10-4m2. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross-section of the rope should be ______.
(take g = 10 ms-2)
Answer in one sentence:
What is an elastomer?
Strain is defined as the ratio of ______.
What are the dimensions of stress?
