Due to global warming, if the ice in the polar region melts and some of this water flows to the equatorial region, then

Statement (I) : The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration. Statement (II) : From a height of \(15 \mathrm{~m}\) a ball is projected vertically upwards with a velocity of \(30 \mathrm{~m} / \mathrm{s}\). If the ball rises to the same height after hitting the ground, the loss of its energy on hitting the ground is \(30 \%\). Statement (III) : The velocity acquired by a body of mass ' \(m\) ' after travelling a fixed distance from rest under the action of a constant force is directly proportional to mass ' \(\mathrm{m}\) '. Which of the following is correct?

A current carrying wire in its neighbourhood produces

A block of material with density \(3 \mathrm{~g} / \mathrm{cc}\) is placed on a fluid of density \(7 \mathrm{~g} / \mathrm{cc}\). The fraction of volume of the piece of material outside the fluid is

Two lenses of power $-1.6$ D and $+2.1$ D respectively are placed in contact. The focal length of the combination is

Identify the correct option.

Two conducting spheres of radii \(r_1\) and \(r_2\) are charged to the same surface charge density. The ratio of electric fields near their surfaces is

A primary coil and secondary coil are placed close to each other. A current, which changes at the rate of \(25 \mathrm{~A}\) in a millisecond, is present in the primary coil. If the mutual inductance is \(92 \times 10^{-6} \mathrm{H}\), then the value of induced emf in the secondary coil is

A large tank filled with water to a height \(h\) is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from \(h\) to \(h / 2\) and \(h / 2\) to zero is

A uniform rod of length \(8 a\) and mass \(6 m\) lies on a smooth horizontal surface. Two point masses \(m\) and \(2 m\) moving in the same plane with speed \(2 v\) and \(v\) respectively strike the rod perpendicularly at distances \(a\) and \(2 a\) from the mid point of the rod in the opposite directions and stick to the rod. The angular velocity of the system immediately after the collision is :

Match the following (Take the relative strength of the strongest fundamental forces in nature as one)
The correct match is

The related effort to derive the properties of a bigger, more complex system from the properties and interactions of its constituent simpler parts is

The mean kinetic energy of monoatomic gas molecules under standard conditions is \(\left\langle E_1\right\rangle\). If the gas is compressed adiabatically 8 times to its initial volume, the mean kinetic energy of gas molecules changes to \(\left\langle E_2\right\rangle\). The ratio \(\frac{\left\langle E_2\right\rangle}{\left\langle E_1\right\rangle}\) is