$A$ body of mass $m=10 \; kg$ is attached to one end of a wire of length $L=0.3 \; m$. The maximum angular speed (in $rad \; s^{-1}$) with which it can be rotated about its other end in a space station is (Breaking stress of wire $= 4.8 \times 10^{7} \; N m^{-2}$ and area of cross-section of the wire $= 10^{-2} \; cm^{2}$)

$A$ man grows into a giant such that his linear dimensions increase by a factor of $9$. Assuming that his density remains the same,the stress in the leg will change by a factor of

Each of three blocks $P$,$Q$ and $R$ shown in the figure has a mass of $3 \,kg$. Each of the wires $A$ and $B$ has a cross-sectional area of $0.005 \,cm^2$ and a Young's modulus of $2 \times 10^{11} \,N \,m^{-2}$. Neglecting friction,the longitudinal strain on wire $B$ is . . . . . . $\times 10^{-4}$. (Take $g=10 \,m/s^2$)

One end of a wire of $8 \,mm$ radius and $100 \,cm$ length is fixed and the other end is twisted through an angle of $45^{\circ}$. The angle of shear is (in $^{\circ}$)

Match the following:

Column-$I$	Column-$II$
$(A)$ Shear modulus	$(I)$ Resistance to change in volume
$(B)$ Shearing stress	$(II)$ Proportionality constant
$(C)$ Elastic fatigue	$(III)$ Tangential stress
$(D)$ Modulus of elasticity	$(IV)$ Temporary loss of elastic property
	$(V)$ Resistance to change against deformation force

The correct match is:

$A$ string of cross-sectional area $4 \times 10^{-6} \, m^{2}$ and length $0.5 \, m$ is connected to a rigid body of mass $2 \, kg$. The body is rotated in a vertical circular path of radius $0.5 \, m$. The body acquires a speed of $5 \, m/s$ at the bottom of the circular path. The strain produced in the string when the body is at the bottom of the circle is $\dots \times 10^{-5}$. (Use Young's modulus $Y = 10^{11} \, N/m^{2}$ and $g = 10 \, m/s^{2}$)