The edge of an aluminium cube is $10\; cm$ long. One face of the cube is firmly fixed to a vertical wall. A mass of $100 \;kg$ is then attached to the opposite face of the cube. The shear modulus of aluminium is $25\; GPa$. What is the vertical deflection of this face?

Young's modules of material of a wire of length ' $L$ ' and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and cross-sectional area is halved then Young's $modules$ will be :

A steel ring of radius $r$ and cross-section area $‘A’$ is fitted on to a wooden disc of radius $R(R > r)$. If Young's modulus be $E,$ then the force with which the steel ring is expanded is

A rigid massless rod of length $6\ L$ is suspended horizontally by means of two elasticrods $PQ$ and $RS$ as given figure. Their area of cross section, young's modulus and lengths are mentioned in figure. Find deflection of end $S$ in equilibrium state. Free end of rigid rod is pushed down by a constant force . $A$ is area of cross section, $Y$ is young's modulus of elasticity

In the given figure, two elastic rods $A$ & $B$ are rigidly joined to end supports. $A$ small mass $‘m’$ is moving with velocity $v$ between the rods. All collisions are assumed to be elastic & the surface is given to be frictionless. The time period of small mass $‘m’$ will be : [$A=$ area of cross section, $Y =$ Young’s modulus, $L=$ length of each rod ; here, an elastic rod may be treated as a spring of spring constant $\frac{{YA}}{L}$ ]