1
JEE Main 2023 (Online) 25th January Evening Shift
Numerical
+4
-1

A spherical drop of liquid splits into 1000 identical spherical drops. If u$$_\mathrm{i}$$ is the surface energy of the original drop and u$$_\mathrm{f}$$ is the total surface energy of the resulting drops, the (ignoring evaporation), $${{{u_f}} \over {{u_i}}} = \left( {{{10} \over x}} \right)$$. Then value of x is ____________ :

2
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45$$^\circ$$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $$x\times10^4$$ Nm$$^{-2}$$. The value of $$x$$ is ___________.

3
JEE Main 2023 (Online) 24th January Evening Shift
Numerical
+4
-1

A Spherical ball of radius 1mm and density 10.5 g/cc is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g/cc. Viscous force on the ball when it attains constant velocity is $$3696\times10^{-x}$$ N. The value of $$x$$ is ________.

(Given, g = 9.8 m/s$$^2$$ and $$\pi=\frac{22}{7}$$)

4
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1

A tube of length $$50 \mathrm{~cm}$$ is filled completely with an incompressible liquid of mass $$250 \mathrm{~g}$$ and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $$x \sqrt{F} \,\mathrm{rad} \,\mathrm{s}^{-1}$$. If $$\mathrm{F}$$ be the force exerted by the liquid at the other end then the value of $$x$$ will be __________.