Mechanical Prop...

Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area $$A$$ and wire 2 has cross- sectional area $$3A$$. If the length of wire 1 increases by $$\Delta \mathrm{x}$$ on applying force $$\mathrm{F}$$, how much force is needed to stretch wire 2 by the same amount  ?

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, $$\left(\displaystyle\frac{dr}{r}\right)$$, is?

A uniformly tapering conical wire is made from a material of Young's modulus $$Y$$ and has a normal, unextended length $$L$$. The radii, at the upper and lower ends of this conical wire, have values $$R$$ and $$3R$$, respectively. The upper end of the wire is fixed to a rigid support and a mass $$M$$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal to:

The Bulk moduli of Ethanol, Mercury and water are given as $$0.9, 25$$ and $$2.2$$ respectively in units of $$10^9/ Nm^{-2}$$. For a given value of pressure, the fractional compression in volume is $$\displaystyle \frac{\Delta V}{V}$$. Which of the following statements about $$\displaystyle \frac{\Delta V}{V}$$ for these three liquids is correct?

If speed(V), acceleration(A) and force(F) are considered as fundamental units, the dimension of Young's modulus will be?

A thin 1 m long rod has a radius of 5 mm.1 A force of 50 $$\pi kN$$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ? 

A bottle has an opening of radius $$a$$ and length $$b$$. A cork of length $$b$$ and radius $$(a+ \Delta a)$$ where $$(\Delta a << a)$$ is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and the frictional coefficient between the bottle and cork is $$\mu$$ then the force needed to push the cork into the bottle is :

A wire fixed at the upper end stretches by length $$l$$ by applying a force $$F$$. The work done in stretching is: 

A wire suspended vertically from one of its ends stretched by attaching a weight of $$200 N$$ to the lower end. The weight stretches the wire by $$1 mm$$. Then the elastic energy stored in the wire is:

A wire elongates by $$1 mm$$ when a load W is hanged from it. lf the wire goes over a pulley and two weights $$\mathrm{W}$$ each are hung at the two ends, the elongation of the wire will be (in mm):