A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is \(7 \times 10^8 \mathrm{~V} / \mathrm{s}\) then the integer value of the distance between the parallel plates is \(\left(\right.\) Take, \(\left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right)\) ________ \(\mu \mathrm{m}\).

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R) : In isothermal process, \(\mathrm{PV}=\) constant, while in adiabatic process \(\mathrm{PV}^\gamma=\) constant. Here \(\gamma\) is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below :

In Young's double slit arrangement, slits are separated by a gap of \(0.5\, mm ,\) and the screen is placed at a distance of \(0.5\, m\) from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of \(5890\, A^o\) is

Five persons \(P_1, P_2, P_3, P_4\) and \(P_5\) recorded object distance (u) and image distance (v) using same convex lens having power +5 D as \((25,96),(30,62)\), \((35,37),(45,35)\) and \((50,32)\) respectively. Identify correct statement

Two cars are approaching each other at an equal speed of \(7.2\, km / hr\). When they see each other, both blow horns having frequency of \(676\, Hz\). The beat frequency heard by each driver will be \(.....\, Hz\). [Velocity of sound in air is \(340\,m / s .]\)

Steel ruptures when a shear of \(3 .5 \times 10^8\,\,N\,m^{-2}\) is applied. The force needed to punch a \(1\,cm\) diameter hole in a steel sheet \(0.3\,cm\) thick is nearly

A hydraulic press can lift \(100\, kg\) when a mass \('m'\) is placed on the smaller piston. It can lift ......... \(kg\) when the diameter of the larger piston is increased by \(4\) times and that of the smaller piston is decreased by \(4\) times keeping the same mass \('m'\) on the smaller piston.

The de-Broglie wavelength associated with the electron in the \(n\, = 4\) level is

A solenoid of length \(0.5 \mathrm{~m}\) has a radius of \(1 \mathrm{~cm}\) and is made up of ' \(m\) ' number of turns. It carries a current of \(5 \mathrm{~A}\). If the magnitude of the magnetic field inside the solenoid is \(6.28 \times 10^{-3} \mathrm{~T}\), then the value of \(m\) is _______.

The torque due to the force \((2 \hat{i}+\hat{j}+2 \hat{k})\) about the origin, acting on a particle whose position vector is \((\hat{i}+\hat{j}+\hat{k})\), would be

Two billiard balls of equal mass \(30 \,{g}\) strike a rigid wall with same speed of \(108\, {kmph}\) (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball \('a'\) and ball \('b'\) by the wall along \('X'\) direction is :

Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius r = 0.1 m. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is __________ m/s. (Assume string does not slip and \( g=10 m/s^{2} \))

The period of oscillation of a simple pendulum is \(T=2\pi \sqrt {\frac{l}{g}} \). Measured value of \(L\) is \(20.0\; cm\) known to \(1\; mm\) accuracy and time for \(100\) oscillations of the pendulum is found to be \(90\ s\) using a wrist watch of \(1\; s\) resolution. The accuracy in the determination of \(g\) is   ........ \(\%\)