Mechanical Prop...

A uniform metal wire ring of mass per unit length & radius $$r$$ has cross sectional area $$S$$.
If $$Y$$ is young's modulus of elasticity and it is rotated with and angular velocity $$\omega$$ about it own axis then approx fractional change in radius is :

A uniform steel wire of length $$3$$ m and area of cross section $$2\ mm^2$$ is extended through $$3$$ mm. Calculate the energy stored in the wire, if the elastic limit is not exceeded. $$(Y_{\rm steel}=20\times 10^{10}\ N/m^2)$$

A student performs an experiment to determine the Young's modulus of wire, exactly $$2 \mathrm { m }$$ long , by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $$0.8 \mathrm { mm }$$ with an uncertainty of $$\pm 0.05 \mathrm { mm }$$ at a load of exactly $$1.0 \mathrm { kg }$$ . The student also measures the diameter of the wire to be $$0.4 \mathrm { mm }$$ with a uncertainty of $$\pm 0.01 \mathrm { mm }$$ . Take $$g = 9.8 \mathrm { M } / \mathrm { s } ^ { 2 }$$ (exact). The Young's modulus obtained from the reading is

A ball of mass m is suspended on a weightless elastic thread whose stiffness factor is k. The ball is lifted so that the thread is not stretched and let fall with zero initial velocity. The maximum stretch of the thread in the process of ball's motion is 

glass,rubber,steel,copper in order of increasing the property of elasticity

A wire is stretched by 0.01 m by a certain force F. Another wire of the same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be:

A thin ring of radius R is made up of a material of density 'p' and Young's modulus Y. If the ring is rotated about its centre in its own place with an angular velocity '$$ \omega $$', then the small increase in radius ($$ ( \Delta R ) $$) of the ring is

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 $$\Delta x$$ on applying forced $$F$$, how much force is needed to stretch wire $$2$$ by the same amount?

Stress S is needed to break a copper wire having radius R. The stress needed to break a copper wire of radius 2R will be :-

A block of mass $$m$$ produces an extension of 9 cm in an elastic spring of length 60 cm when it is hung by it, and the system is in equilibrium. The spring is cut in two parts of 40 cm and 20 cm lengths. The same block hangs in equilibrium with the help of these two parts connected in parallel. Find the extension (in cm) in this case.