$A$ force $F$ is needed to break a copper wire having radius $R$. The force needed to break a copper wire of radius $2R$ will be

$A$ wire of density $3 \times 10^3 \, kg/m^3$ requires a breaking stress of $10^6 \, N/m^2$ to break. What should be the length of the wire so that it breaks under its own weight? (Take $g = 10 \, m/s^2$)

$A$ uniform wire of length $l$ and weight $w$ is suspended from the roof with a weight $W$ attached at the other end. The stress in the wire at a distance $l/3$ from the top is given by $(\frac{W}{A} + \gamma \frac{w}{A})$, where $A$ is the cross-sectional area of the wire. The value of $\gamma$ is . . . . . . .

Write the formula,dimensional formula,and $SI$ unit for the Shear Modulus and the Bulk Modulus.

Mark the wrong statement.

$A$ bob of mass $10\, kg$ is attached to a wire $0.3\, m$ long. Its 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 ....... $rad/sec$.