$A$ 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 ............ $^{\circ} C$.
- A$15$
- B$12$
- C$5$
- D$0$
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View SolutionIn the given figure,two elastic rods $A$ and $B$ 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 and the surface is frictionless. The time period of the small mass $m$ will be: [Here,an elastic rod may be treated as a spring of spring constant $k = \frac{YA}{L}$]
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View SolutionStatement $(A)$ For an ideal liquid,the bulk modulus is infinite and the shear modulus is zero.
Statement $(B)$ The volume contraction of a metal cube of bulk modulus $140 \text{ GPa}$ and side length $10 \text{ cm}$,when subjected to a hydraulic pressure of $7 \times 10^6 \text{ Pa}$,is $-0.05 \text{ m}^3$.
Statement $(C)$ $A$ spiral spring is stretched by a weight attached to it. The strain is tensile.
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Match the following:
Column $I$ Column $II$ $A$. Hooke's law $1$. Tangential strain $B$. Shearing strain $2$. Temporary loss of elastic property $C$. Bulk strain $3$. Elastic limit $D$. Elastic fatigue $4$. $3$ times the linear strain
| Column $I$ | Column $II$ |
|---|---|
| $A$. Hooke's law | $1$. Tangential strain |
| $B$. Shearing strain | $2$. Temporary loss of elastic property |
| $C$. Bulk strain | $3$. Elastic limit |
| $D$. Elastic fatigue | $4$. $3$ times the linear strain |
Two blocks of masses $1 \, kg$ and $2 \, kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 \, N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 \, m/s^2$.
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