Mechanical Prop...

When the tension in a metal wire is $${T}_{1}$$, its length is $${l}_{1}$$. When the tension is $${T}_{2}$$, its length is $${l}_{2}$$. The natural length of wire is

A wire stretched $$1mm$$ by a force of $$1kN$$. How far would a wire of the same material and length but of four times that diameter be stretched by the same force?

Bulk modulus of water is $$2\times 10^{9}N/m^{2}$$. The change in pressure required to increase the density of water by $$0.1\%$$ is

Two identical wires of iron and copper with their Young's modulus in the ratio $$3:1$$ are suspended at same level. They are to be loaded so as to have the same extension and hence level. Ratio of the weight is

A ball falling in a lake of depth $$200\ m$$ shows a decrease of $$0.1\%$$ in its volume at the bottom. The bulk modulus of the elasticity of the material of the ball is (take $$g = 10\ m/s^{2})$$.

A long wire hangs vertically with its upper end clamped. A torque of $$8\ Nm$$ applied to the free end twists it through $$45^{\circ}$$. The potential energy of the twisted wire is

Young's modulis of brass and steel are $$10\times 10^{10} N/m$$ and $$2\times 10^{11} N/m^{2}$$, respectively. A brass wire and a steel wire of the same length are extended by $$1\ mm$$ under the same force. The radii of the brass and steel wires are $$R_{B}$ and $$R_{S}$$, respectively. Then

A long elastic spring is stretched by $$2\ cm$$ and its potential energy is $$U$$. If the spring is stretched by $$10\ cm$$, the P.E., will be

Two wires of the same material and same mass are stretched by the same force. Their length are in the ratio $$2:3$$. Their elongations are in the ratio

Each of the pictures shows four objects tied together with rubber bands being pulled to the right across a horizontal frictionless surface by a horizontal force $$F$$. All the objects have the same mass; all the rubber bands obey Hooke's law and have the same equilibrium length and the same force constant. Which of these pictures is drawn most correctly?