When a $4\, kg$ mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by $2\, cms$. The work required to be done by an external agent in stretching this spring by $5\, cms$ will be ......... $joule$ $(g = 9.8\,metres/se{c^2})$
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Two wires of the same material (Young's modulus $Y$ ) and same length $L$ but radii $R$ and $2R$ respectively are joined end to end and a weight $W$ is suspended from the combination as shown in the figure. The elastic potential energy in the system is
Which of the following curve represents the correctly distribution of elongation $(y)$ along heavy rod under its own weight $L \rightarrow$ length of rod, $x \rightarrow$ distance of point from lower end?
The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} m ^{2}$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to $25$ metric tons, the required area of cross section of the rope should be.$.........\times 10^{-4} \,m ^{2}$ (take $g =10\, ms ^{-2}$ )
If average depth of an ocean is $4000 \mathrm{~m}$ and the bulk modulus of water is $2 \times 10^9 \mathrm{Nm}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is ___________(Given, $\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ )
The bulk modulus of rubber is $9.1 \times 10^8\,N/m^2$. To what depth a rubber ball be taken in a lake so that its volume is decreased by $0.1\%$ ? ....... $m$
The ratio of diameters of two wires of same material is $n : 1$. The length of wires are $4\, m$ each. On applying the same load, the increase in length of thin wire will be