1
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1

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, $$\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$$)

2
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
There is an air bubble of radius $1.0 \mathrm{~mm}$ in a liquid of surface tension $0.075~ \mathrm{Nm}^{-1}$ and density $1000 \mathrm{~kg} \mathrm{~m}^{-3}$ at a depth of $10 \mathrm{~cm}$ below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _________ $\mathrm{Pa}\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$
3
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1

The elastic potential energy stored in a steel wire of length $$20 \mathrm{~m}$$ stretched through $$2 \mathrm{~cm}$$ is $$80 \mathrm{~J}$$. The cross sectional area of the wire is __________ $$\mathrm{mm}^{2}$$.

$$\left(\right.$$ Given, $$\left.y=2.0 \times 10^{11} \mathrm{Nm}^{-2}\right)$$

4
JEE Main 2023 (Online) 12th April Morning Shift
Numerical
+4
-1

Glycerin of density $$1.25 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$$ is flowing through the conical section of pipe The area of cross-section of the pipe at its ends are $$10 \mathrm{~cm}^{2}$$ and $$5 \mathrm{~cm}^{2}$$ and pressure drop across its length is $$3 ~\mathrm{Nm}^{-2}$$. The rate of flow of glycerin through the pipe is $$x \times 10^{-5} \mathrm{~m}^{3} \mathrm{~s}^{-1}$$. The value of $$x$$ is ___________.