$A$ body of mass $10 \ kg$ is attached to a wire of $0.3 \ m$ length. The breaking stress is $4.8 \times 10^7 \ N \ m^{-2}$. The area of cross-section of the wire is $10^{-6} \ m^2$. The maximum angular velocity with which it can be rotated in a horizontal circle is

The two thigh bones (femurs),each of cross-sectional area $10 \; cm^{2}$,support the upper part of a human body of mass $40 \; kg$. Estimate the average pressure sustained by the femurs.

$A$ metal rod of cross-sectional area $10^{-4} \, m^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \, K^{-1}$ and its Young's modulus is $4 \times 10^{12} \, N/m^{2}$. When the temperature of the chamber is lowered to $T$,a weight of $5000 \, N$ needs to be attached to the rod so that its length remains unchanged. Then,$T$ is ............ $^{\circ} C$.

For the tensile stress on the cross-section $PQRS$ to be maximum,$\theta =$ ......... $^o$

In order to determine the Young's Modulus of a wire of radius $0.2 \, cm$ (measured using a scale of least count $= 0.001 \, cm$) and length $1 \, m$ (measured using a scale of least count $= 1 \, mm$),a weight of mass $1 \, kg$ (measured using a scale of least count $= 1 \, g$) was hanged to get the elongation of $0.5 \, cm$ (measured using a scale of least count $= 0.001 \, cm$). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in $\%$)

What is the tangential stress on the cross-section $PQRS$?