An massless equilateral triangle \(EFG\) of side \('a'\) (As shown in figure) has three particles of mass \(m\) situated at its vertices. The moment of intertia of the system about the line \(EX\) perpendicular to \(EG\) in the plane of \(EFG\) is \(\frac{ N }{20}\, ma ^{2}\) where \(N\) is an integer. The value of \(N\) is

A person is standing in an elevator. In which situation, he experiences weight loss?

A plane electromagnetic wave in a non-magnetic dielectric medium is given by \(\vec E\, = \,{\vec E_0}\,(4 \times {10^{ - 7}}\,x - 50t)\) with distance being in meter and time in seconds. The dielectric constant of the medium is

Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{\mathrm{~L}^2}\), the length of the sides of the square is _______.

A circular current loop of radius \(R\) is placed inside square loop of side length \(L\) \((L >> R)\) such that they are co-planar and their centers coincide. The permeability of free space is \(\mu_0\). The mutual inductance between circular loop and square loop is _______.

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are \(0.1 \;kg - m ^{2}\) and \(10\; rad \,s^{-1}\) respectively while those for the second one are \(0.2 \;kg - m ^{2}\) and \(5\; rad \,s ^{-1}\) respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The Kinetic energy of the combined system is ...........\(J\)

A disc of mass \(1\,kg\) and radius \(R\) is free of rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be \(4 \sqrt{\frac{x}{3 R}}\) rad s\(^{-1}\) where \(x=\) \(\left( g =10\,ms ^{-2}\right)\)

Choose the correct relationship between Poisson ratio \((\sigma)\). bulk modulus \(( K )\) and modulus of rigidity \((\eta)\) of a given solid object:

Consider following statements:
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid.
B. As the temperature of liquid rises, the coefficient of viscosity increases.
C. As the temperature of gas increases, the coefficient of viscosity increases
D. The onset of turbulence is determined by Reynold's number.
E. In a steady flow two stream lines never intersect.
Choose the correct answer from the options given below:

Two masses \(m\) and \(\frac{m}{2}\) are connected at the two ends of a massless rigid rod of length \(l\). The rod is suspended by a thin wire of torsional constant \(k\) at the centre of mass of the rodmass system (see figure). Because of torsional constant \(k\), the restoring torque is \(\tau  = k\,\theta \) for angular displacement \(\theta \). If the rod is rotated by \(\theta _0\) and released, the tension in it when it passes through its mean position will be

A stone tied to \(180 cm\) long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is \(\frac{1936}{ x }\,ms ^{-2}\). The value of \(x.........\left(\text { Take } \pi=\frac{22}{7}\right)\)