1
JEE Main 2024 (Online) 31st January Morning Shift
Numerical
+4
-1

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $$0.02 \%$$ is _______ $$m$$.

(Take density of sea water $$=10^3 \mathrm{kgm}^{-3}$$, Bulk modulus of rubber $$=9 \times 10^8 \mathrm{~Nm}^{-2}$$, and $$g=10 \mathrm{~ms}^{-2}$$)

2
JEE Main 2024 (Online) 30th January Evening Shift
Numerical
+4
-1

A big drop is formed by coalescing 1000 small identical drops of water. If $$E_1$$ be the total surface energy of 1000 small drops of water and $$E_2$$ be the surface energy of single big drop of water, then $$E_1: E_2$$ is $$x: 1$$ where $$x=$$ ________.

3
JEE Main 2024 (Online) 30th January Morning Shift
Numerical
+4
-1

Each of three blocks $$\mathrm{P}, \mathrm{Q}$$ and $$\mathrm{R}$$ shown in figure has a mass of $$3 \mathrm{~kg}$$. Each of the wires $$\mathrm{A}$$ and $$\mathrm{B}$$ has cross-sectional area $$0.005 \mathrm{~cm}^2$$ and Young's modulus $$2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$. Neglecting friction, the longitudinal strain on wire $$B$$ is ________ $$\times 10^{-4}$$. (Take $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$)

4
JEE Main 2024 (Online) 29th January Evening Shift
Numerical
+4
-1

Two metallic wires $$P$$ and $$Q$$ have same volume and are made up of same material. If their area of cross sections are in the ratio $$4: 1$$ and force $$F_1$$ is applied to $$P$$, an extension of $$\Delta l$$ is produced. The force which is required to produce same extension in $$Q$$ is $$\mathrm{F}_2$$.

The value of $$\frac{F_1}{F_2}$$ is _________.