The time period of a satellite revolving around earth in a given orbit is \(7 \,hours\). If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be ...... \(hours\)

A monochromatic source of light operating at \(15\) kW emits \(2.5\times 10^{22}\) photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ________. (Take \(h=6.6\times 10^{-34}\) J·s and \(c=3\times 10^8\) m/s).

Three parallel plate capacitors \(\mathrm{C}_1, \mathrm{C}_2\) and \(\mathrm{C}_3\) each of capacitance \(5 \mu \mathrm{~F}\) are connected as shown in figure. The effective capacitance between points A and B, when the space between the parallel plates of \(C_1\) capacitor is filled with a dielectric medium having dielectric constant of 4, is :

A ball of mass 100 g is projected with velocity \(20 \mathrm{~m} / \mathrm{s}\) at \(60^{\circ}\) with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

A point charge of magnitude \(+ 1\,\mu C\) is fixed at \((0, 0, 0) \). An isolated uncharged spherical conductor, is fixed with its center at \((4, 0, 0).\) The potential and the induced electric field at the centre of the sphere is

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure (P), temperature (T) and density ( \(\rho\) ) are intensive variables.
(C) Volume (V), temperature (T) and density ( \(\rho\) ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

A car is moving on a horizontal curved road with radius \(50\,m\). The approximate maximum speed of car will be \(............\,ms^{-1}\), if friction between tyres and road is \(0.34.\left[\right.\) Take \(\left.g =10 ms ^{-2}\right]\)

A metal block of mass \(m\) is suspended from a rigid support through a metal wire of diameter \(14\,mm\). The tensile stress developed in the wire under equilibrium state is \(7 \times 10^5\,Nm ^{-2}\). The value of mass \(m\) is \(......kg\). (Take, \(g =9.8\,ms ^{-2}\) and \(\left.\pi=\frac{22}{7}\right)\)

If speed \(V,\) area \(A\) and force \(F\) are chosen as fundamental units, then the dimension of Young's modulus will be :

A block of mass \(5 \mathrm{~kg}\) is placed on a rough inclined surface as shown in the figure.If \(\vec{F}_1\) is the force required to just move the block up the inclined plane and \(\vec{F}_2\) is the force required to just prevent the block from sliding down, then the value of \(\left|\vec{F}_1\right|-\left|\vec{F}_2\right|\) is _______. [Use \(g=10 \mathrm{~m} / \mathrm{s}^2\) ]

Given below are two statements: Statement \(I\) : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates \(EM\) waves. Statement \(II\) : In a material medium. The \(EM\) wave travels with speed \(v =\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}\). In the light of the above statements, choose the correct answer from the options given below