Mechanical Prop...

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

A steel rod of cross sectional area $$1 m^2$$ is acted upon by forces shown in the fig. Determine the total elongation of the bar. ($$Y = 2.0 \times 10^{11} N/m^2$$)

What force should be applied to the ends of steel rod of a cross sectional area  $$10 { cm } ^ { 2 }$$  to prevent it from elongation when heated from  $$273 { K }$$  to  $$303 { K }$$  ? ( $$\alpha$$  of steel  $$10^{ { -5 } }\quad ^{ 0 }{ { C }^{ -1 } },Y=2\times 10^{ { 11 } }{ Nm }^{ { -2 } }$$ )

In the young's double slit experiments, the intensities at two points $$ P_1 $$ and $$ P_2 $$ on the screen are respectively.$$ I_1 $$ and $$ I_2 $$. If $$ P_1 $$ is located at the centre of a bright fringe and $$ P_2 $$ is located at a distance equal to a quarter of fringe width from $$ P_1$$, then $$ \frac {I_1}{I_2} $$ is

If uniform rod of length  $$5 { m },$$  area of cross-section  $$50{ cm }^{ { 2 } }$$  and Young's modulus  $$4 \times 10 ^ { 9 }  { Pa }$$  is lying at rest under the action of forces as shown, then the total extension in the rod is

In the question $$22$$, when is the tensile stress maximum ?

A uniform steel rod of length 1m and area of cross section 20 $$ c{ m }^{2  } $$ is hanging from a fixed support. Find the increase in the length of the rod.
$$ ({  Y}_{ steel }=2.0\times 1{0  }^{ 11 }N{m  }^{ -2 }, {P  }_{ steel }= 7.85\times 1{0  }^{ 3 }kg{m  }^{-3  }) $$

A uniform wire fixed at its upper end hangs vertically and supports a weight at its lower end. If its radius is r, length is L and the Young's modulus for the material of the wire is E then extension produced in the wire is

A steel wire of length 4 m and diameter 5 mm is stretched by 5 kgwt. The increase in its length , if the Young's modulus of steel wire is $$2.4 \times { 10 }^{ 12 } dyne/{ cm }^{ 2 }$$. is

A body of mass 10 kg is attached to a 0.3 m long wire of cross area $${ 10 }^{ 6 }$$ $${ m }^{ 2 }$$ Breaking steers of the wire if $$4.8\times { 10 }^{ 7 }$$ What is the maximum angular velocity with which it can be rotated in a horizontal circle?