If a brass sphere of radius 36 cm is submerged in a lake at a depth where the pressure is $10^7 \mathrm{~Pa}$, then the change in the radius of the sphere is

(Bulk modulus of brass $=60 \mathrm{GPa}$ )

A simple pendulum is made of a metal wire of length $L$, area of cross-section $A$, material of Young's modulus $Y$ and a bob of mass $m$. This pendulum is hung in abus moving with a uniform speed $v$ on a horizontal circular road of radius $R$. The elongation in the wire is

A wire of cross-sectional area $10^{-6} \mathrm{~m}^{2}$ is elongated by $0.1 \%$ when the tension in it is 1000 N . The Young's modulus of the material of the wire is (assume radius of the wire is constant)

A block of mass 2 kg is tied to one end of a 2 m long metal wire of $1.0 \mathrm{~mm}^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is 2 mm , the Young's modulus of the metal is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )