An iron rod of length 2m and cross-sectional area of 50 mm² stretched by 0.5 mm, when amass of 250 kg is hung from its lower end. Young’s modulus of iron rod is

19.6 × 10²⁰ N/m²
19.6 × 10¹⁸ N/m²
19.6 × 10¹⁰ N/m²
19.6 × 10¹⁵ N/m²

Solution

A beam of metal supported at the two edges is loaded at the centre. The depression at the centre is proportional to

Y²
Y
1/Y
1/Y²

Solution

One end of a uniform wire of length L and of weight W is attached rigidly to apoint in the roof and W₁ weight is suspended from looser end. If A is area of cross-section of the wire, the stress in the wire at a height ^L⁄₄ from the upper end is

\(\frac{W_{1}+W}{a}\)
\(\frac{W_{1}+3W/4}{a}\)
\(\frac{W_{1}+W/4}{a}\)
\(\frac{4W_{1}+3W}{a}\)

From a steel wire of density ρ is suspended a brass block of density ρ_b. The extension of steel wire comes to e. If the brass block is now fully immersed in a liquid of density ρ_l,the extension becomes e’. The ratio ^e⁄_e’ will be

\(\frac{\rho b}{\rho _{b}-\rho _{\iota }}\)
\(\frac{\rho _{b}-\rho _{\iota }}{\rho _{b}}\)
\(\frac{\rho _{b}-\rho}{\rho _{l}- \rho }\)
\(\frac{\rho _{l}}{\rho _{b}- \rho_{l} }\)

Solution

Weights without and with liquid proportional to ρ_b and ρ_b– ρ_l.

A circular tube of mean radius 8 cm and thickness 0.04 cm is melted up and recast into a solid rod of the same length.The ratio of the torsional rigidities of the circular tube and the solid rod is

\(\frac{(8.02)^{4}-(7.98)^{4}}{(0.8)^{4}}\)
\(\frac{(8.02)^{2}-(7.98)^{2}}{(0.8)^{2}}\)
\(\frac{(0.8)^{2}}{(8.02)^{4}-(7.98)^{4}}\)
\(\frac{(0.8)^{2}}{(8.02)^{3}-(7.98)^{3}}\)

Solution

A massive stone pillar 20 m high and of uniform cross-section rests on a rigid base and supports a vertical load of 5.0 × 10⁵ N at its upper end. If the compressive stress in the pillar is not to exceed 1.6 × 10⁶ N m^-2, what is the minimum cross-sectional area of the pillar? Density of the stone =2.5× 10³kgm^-3. (Take g =10 N kg^-1)

0.15 m²
0.25 m²
0.35 m²
0.45 m²

Solution

For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular cross-section is

3: π
π: 3
1: π
π: 1

Solution

A steel wire is suspended vertically from a rigid support.When loaded with a weight in air,it extends by l_a and when the weight is immersed completely in water,the extension is reduced to l_w. Then the relative density of material of the weight is

\(\iota _{a}/\iota _{w}\)
\(\frac{\iota _{a}}{\iota _{a}-\iota _{w}}\)
\(\iota _{w}/(\iota _{a}-\iota _{w})\)
\(\iota _{w}/\iota _{a}\)

Solution

A cube at temperature 0º C is compressed equally from all sides by an external pressure P.By what amount should its temperature be raised to bring it back to the size it had before the external pressure was applied. The bulk modulus of the material of the cube is Band the coefficient of linear expansion is α.

P/B α
P/3 Bα
3 π α/B
3 B/P

Solution

A steel ring of radius r and cross sectional area A is fitted onto a wooden disc of radius R (R > r). If the Young’s modulus of steel is Y,then the force with which the steel ring is expanded is

A Y (R/r)
A Y (R – r)/r
(Y/A)[(R – r)/r]
Y r/A R

Solution

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