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.
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.
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?
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 ?
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 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
Answer in one sentence.
How should be a force applied on a body to produce shearing stress?
A charged particle is moving in a uniform magnetic field in a circular path of radius R. When the energy of the particle becomes three times the original, the new radius will be ______.
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 ______.
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.
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?
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?
