Consider a cylindrical tank of radius $$1 \mathrm{~m}$$ is filled with water. The top surface of water is at $$15 \mathrm{~m}$$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $$5 \mathrm{~m}$$ from the bottom. A force of $$5 \times 10^{5} \mathrm{~N}$$ is applied an the top surface of water using a piston. The speed of ifflux from the hole will be : (given atmospheric pressure $$\mathrm{P}_{\mathrm{A}}=1.01 \times 10^{5} \mathrm{~Pa}$$, density of water $$\rho_{\mathrm{W}}=1000 \mathrm{~kg} / \mathrm{m}^{3}$$ and gravitational acceleration $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$ )

A balloon has mass of $$10 \mathrm{~g}$$ in air. The air escapes from the balloon at a uniform rate with velocity $$4.5 \mathrm{~cm} / \mathrm{s}$$. If the balloon shrinks in $$5 \mathrm{~s}$$ completely. Then, the average force acting on that balloon will be (in dyne).

The force required to stretch a wire of cross-section $$1 \mathrm{~cm}^{2}$$ to double its length will be : (Given Yong's modulus of the wire $$=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$$)

A steel wire of length $$3.2 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{s}}=2.0 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$$ and a copper wire of length $$4.4 \mathrm{~m}\left(\mathrm{Y}_{\mathrm{c}}=1.1 \times 10^{11} \,\mathrm{Nm}^{-2}\right)$$, both of radius $$1.4 \mathrm{~mm}$$ are connected end to end. When stretched by a load, the net elongation is found to be $$1.4 \mathrm{~mm}$$. The load applied, in Newton, will be: $$\quad\left(\right.$$ Given $$\pi=\frac{22}{7}$$)