Mechanical Prop...

A uniform rod of mass m, length L, area of cross-section A and Youngs modulus Y hangs from a rigid support. Its elongation under its own weight will be:

Calculate the extension of the steel wire and the energy stored in it.

A steel rope has length $$L$$, area of cross-section $$A$$, Young's modulus $$Y$$. [$$Density = d$$]. If the steel rope is vertical and moving with the force acting vertically up at the upper end, find the strain at a point $$\displaystyle \frac{L}{3}$$ from lower end.

A slightly conical wire of length L and end radii $$r_1$$ and $$r_2$$ is stretched by two forces F and F applied parallel to the length in opposite directions and normal to the end faces. If Y denotes Young's modulus, then the extension produced is:

The speed of a traverse wave travelling on a wire having a length $$50\space cm$$ and mass $$50\space g$$ is $$80\space ms^{-1}$$. The area of cross-section of the wire is $$1\space mm^2$$ and its Young's modulus is $$16\times10^{11}\space Nm^{-2}$$. Find the extension of the wire over natural length.

A ball of radius R and with bulk modulus of elasticity K is kept in a liquid inside a cylindrical container. It is pressed by putting a mass m on a massless piston of cross-sectional area A, then the fractional decrease in the radius of ball will be

A small solid sphere of radius R made of a material of bulk modulus B is surrounded by an incompressible liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. The magnitude of fractional change in the radius of the sphere $$\left( \dfrac{dR}{R} \right)$$when a mass M is placed slowly on the piston to compress the liquid is:

Six identical uniform rods $$PQ, QR, RS, ST, TU$$ and $$UP$$ each weighing W are freely joined at their ends to form a hexagon. The rod $$PQ$$ is fixed in a horizontal position and middle points of $$PQ$$ and $$ST$$ are connected by a vertical string. The tension in string is

Two opposite forces $$F_1 = 120N \:and \:F_2 = 80N$$ act on an heavy elastic plank of modulus of elasticity $$y=2\times 10^{11}N/m^2$$ and length $$L = 1m$$ placed over a smooth horizontal surface. The cross-sectional area of plank is $$A = 0.5m^2$$. If the change in the length of plank is (in nm )