The escape velocity of a body on a planet  \('A'\)  is \(12 \,kms ^{-1}\). The escape velocity of the body on another planet  \('B'\) , whose density is four times and radius is half of the planet  \('A'\), is ................... \(kms ^{-1}\)

Two wires A and B are made of same material having ratio of lengths \(\frac{L_A}{L_B}=\frac{1}{3}\) and their diameters ratio \(\frac{d_A}{d_B}=2\). If both the wires are stretched using same force, what would be the ratio of their respective elongations?

The current in a conductor is expressed as \(I=3 t^2+4 t^3\), where \(I\) is in Ampere and \(t\) is in second. The amount of electric charge that flows through a section of the conductor during \(t=1\) s to \(t=2 \mathrm{~s}\) is _______ \(\mathrm{C}\).

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet.
In the light of the above statements, choose the correct answer from the options given below :

Visible light of wavelength \(6000 \times 10^{-8}\; \mathrm{cm}\) falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at \(60^{\circ}\) from the central maximum. If the first minimum is produced at \(\theta_{1},\) then \(\theta_{1}\) is close to.....\(^o\)

The amplitude of magnetic field in an electromagnetic wave propagating along \(y\)-axis is \(6.0 \times 10^{-7}\,T\). The maximum value of electric field in the electromagnetic wave is:

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A :\) Photodiodes are preferably operated in reverse bias condition for light intensity measurement. Reason \(R\) : The current in the forward bias is more than the current in the reverse bias for a \(p - n\) junction diode. In the light of the above statement, choose the correct answer from the options given below :

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

Assuming human pupil to have a radius of \(0.25\ cm\) and a comfortable viewing distance of \(25\ cm\), the minimum separation between two objects that human eye can resolve at \(500\ nm\) wavelength is.....\(\mu m\)