In an experiment, brass and steel wires of length \(1~\text{m}\) each with areas of cross section \(1~\text{mm}^2\) are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of \(0.2~\text{mm}\) is, [Given, the Young's Modulus for steel and brass are, respectively, \(120 \times 10^9 ~\text{N/m}^2\) and \(60 \times 10^9 ~\text{N/m}^2\)]
1. \( 4.0 \times 10^6 ~\text{N/m}^2\)
2. \( 1.2 \times 10^6~\text{N/m}^2\)
3. \( 1.8 \times 10^6~\text{N/m}^2\)
4. \(8 \times 10^6~\text{N/m}^2\)

The elastic limit of brass is 400 MPa. What should be the minimum diameter of a brass rod if it is to support a 400\(\pi \) N load without exceeding its elastic limit?
1. 1 mm
2. 1.5 mm
3. 2 mm
4. 2.5 mm

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 the entire cross-section of the 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, \( \left (\dfrac{dr}{r} \right ) \) is:

The normal density of a material is \(\rho\) and its bulk modulus of elasticity is \(K\). The magnitude of the increase in the density of material when a pressure \(P\) is applied uniformly on all sides, will be:

A uniform metallic wire is elongated by \(0.04\) m when subjected to a linear force \(F\). The elongation, if its length and diameter are doubled and subjected to the same force will be:

A cube of metal is subjected to a hydrostatic pressure of \(4~\text{GPa}\). The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, \(B=8 \times 10^{10} ~\text{Pa}\))
1. \(5\)
2. \(20\)
3. \(0.6\)
4. \(1.67\)

A man transforms into a giant such that all his linear dimensions become \(9\) times their original values. Assuming his density remains unchanged, the stress on his legs changes by a factor of:

A boy’s catapult is made of a rubber cord \(42~\text{cm}\) long and \(6~\text{mm}\) in diameter. Placing a\(0.02~\text{kg}\) stone on it, the boy stretches the cord by \(20~\text{cm}\) using a constant force. When released, the stone moves off with a velocity of \(20\) m/s. Neglecting the change in cross-sectional area while stretching, the Young’s modulus of the rubber is approximately equal to:
1. \( 10^3 ~\text{N-m}^{-2} \)
2. \(10^4~\text{N-m}^{-2} \)
3. \( 10^6 ~\text{N-m}^{-2} \)
4. \( 10^8~\text{N-m}^{-2} \)