Mechanical Prop...

A mass m is hanging from a wire of cross sectional are A and length L. Y is young's modulus of wire. An external force F is applied on he wire which is then slowly further pulled down by $$\triangle x$$ from its equilibrium position. Find the work done by the force F that the wire exerts on the mass:

 A mild steel wire of length $$2l$$ meter cross-sectional area $$A\,{m^2}$$ is fixed horizontally between two pillars. A small mass $$m \ kg$$ is suspended from the mid point of the wire. If extension in wire are within elastic limit. Then depression at the mid point of wire will be

A uniform rod of length L, has a mass per unit length $$\lambda$$ and area of cross-section A. The elongation in the rod is l due to its own weight, if it is suspended from the ceiling of a room.The Young's modulus of the rod is 

A metallic ring of radius $$2cm$$ and cross sectional area $$4cm^{2}$$ is fitted into a wooden circular disc of radius $$4cm$$.If the Young's module of the material of the ring is $$2 \times 10^{11}N/m^2$$, the metal ring expand is:

Two wires of equal length and cross-section are suspended as shown in figure. Their young's modulus are $$Y_1$$ and $$Y_2$$ respectively. Their equivalent young's modulus of elasticity is :

The Young's modulus of brass and steel are respectively $$1.0\times {10}^{10}N/{m}^{2}$$ and $$2\times {10}^{10}N/{m}^{2}$$. A brass wire and a steel wire of the same length are extended by $$1\ mm$$ under the same force, the radii of brass and steel wires are $${R}_{B}$$ and $${R}_{S}$$ respectively. Then 

A solid sphere of radius R made of a material of bulk modulus B surrounded by a liquid in a cylindrical container.A massless  piston of area A floats on the surface of the liquid. Find the fractional decreases in the radius of the sphere $$ \left( \frac { d R }{ R }  \right)  $$ when a mass M is placed on the piston to compress the liquid:

A neutron moving with a velocity $$v$$ and kinetic energy $$E$$ collides perfectly elastically head on with the nucleus of an atom of mass number $$A$$ at rest. The energy received by the nucleus and the total energy of the system are related by

When a $$20g$$ mass hangs attached to one end of a light spring of length $$10cm$$, the spring stretches by $$2cm$$. The mass is pulled down unitl the total length of the spring is $$14cm$$. The elastic energy, in Joule stored in the spring is -

One end of a uniform rod of mass $$M$$ and cross-sectional area $$A$$ is suspended from the other end. The stress at the mid-point of the rod will be :