EASY
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Why is strain Unitless?

Important Questions on Mechanical Properties of Solids

MEDIUM
A body of mass m=10 kg is attached to one end of a wire of length 0.3 m. What is the maximum angular speed (in rad s-1) with which it can be rotated about its other end in a space station without breaking the wire?
[Breaking stress of wire σ=4.8×107 N m-2 and area of cross-section of the wire=10-2 cm2]
MEDIUM
An elevator of mass m  is connected to a rope which pulls the elevator up with a maximum acceleration equal to a . If the maximum bearable tension in the rope is T , then for a safe journey the minimum diameter of the rope is [ g = acceleration due to gravity]
EASY
A and B are two wires. The radius of A is twice that of B. They are stretched by the same load. Then the stress on B is
HARD

A mild steel wire of length 2 L and cross-sectional area A is stretched, well with in the elastic limit, horizontally between two pillars as shown in figure. A mass m is suspended from the mid-point of the wire. Strain in the wire is

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HARD
A lift is tied with thick iron ropes having mass M. The maximum acceleration of the lift is ‘a m s-2 and maximum safe stress is S N m-2. The minimum diameter of the rope is
EASY
A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of:
EASY
If a tensile force is suddenly removed from a wire then its temperature will
EASY
The length of metallic wire is l1 when tension in it is T1. It is l2 when the tension is T2. The original length of the wire will be :
EASY
A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be _________ cm.
MEDIUM
A wire of length 1 m and radius 2 mm is vertically clamped. The lower end is twisted through an angle of 45°. The angle of shear is _____
EASY
A cube of metal is subjected to a hydrostatic pressure 4 GPa. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, B=8×1010 Pa)
EASY
The speed of the water in a river is V near the surface. If the coefficient of viscosity of water is η and the depth of the river is H, then the shearing stress between the horizontal layers of water is
MEDIUM
In an experiment, brass and steel wires of length 1 m each with areas of cross section 1 mm2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is,
[Given, the Young's Modulus for steel and brass are, respectively, 120×109 N/m2 and 60×109 N/m2 ]
EASY
Two wires A and B are stretched by the same load. If the area of cross-section of wire 'A' is double that of  'B', then the stress on 'B' is
MEDIUM

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is 24π×102 N m-2. What is the minimum radius of the wire ?
( take g=10 m s-2

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MEDIUM

The two blocks P and Q are connected by a metal wire with breaking stress 109 N m-2 through a frictionless pulley. The minimum radius of the wire for it not to break is (consider g=10 m s-2)

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MEDIUM
A rubber (eraser) 3cm×1cm×8cm is clamped at one end with 8cm edge vertical. A horizontal force of 2.4N is applied at the free end (the top face). If the shear modulus of the rubber is 1.6×105Nm2, then the horizontal displacement of the top face will be
MEDIUM
The length of a metal wire is l1 when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is,
EASY
A steel wire having a radius of 2.0 mm , carrying a load of 4 kg, is hanging from a ceiling. Given that g=3.1π s-2, what will be the tensile stress that would be developed in the wire?