A spherical ball of radius \(1 \times 10^{-4} \mathrm{~m}\) and density \(10^5\) \(\mathrm{kg} / \mathrm{m}^3\) falls freely under gravity through a distance \(h\) before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of \(h\) is approximately _______. (The coefficient of viscosity of water is \(9.8 \times 10^{-6}\) \(\left.\mathrm{N} \mathrm{s} / \mathrm{m}^2\right)\)

A parallel plate capacitor of capacitance \(1 \mu \mathrm{~F}\) is charged to a potential difference of 20 V . The distance between plates is \(1 \mu \mathrm{~m}\). The energy density between plates of capacitor is _________.

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is \((A)\) directly proportional to the length of the potentiometer wire \((B)\) directly proportional to the potential gradient of the wire \((C)\) inversely proportional to the potential gradient of the wire \((D)\) inversely proportional to the length of the potentiometer wire Choose the correct option for the above statements:

An electron with kinetic energy \(5 \mathrm{eV}\) enters a region of uniform magnetic field of \(3 \mu \mathrm{T}\) perpendicular to its direction. An electric field \(\mathrm{E}\) is applied perpendicular to the direction of velocity and magnetic field. electron moves along the same path, The value of \(\mathrm{E}\) is _______ \(\mathrm{NC}^{-1}\). (Given, mass of electron \(=9 \times 10^{-31} \mathrm{~kg}\), electric charge \(=1.6 \times 10^{-19} \mathrm{C}\) )

A body of mass \(1\,kg\) falls freely from a height of \(100\,m,\) on a platform of mass \(3\,kg\) which is mounted on a spring having spring constant \(k = 1.25 \times 10^6\, N/m.\) The body sticks to the platform and the spring’s maximum compression is found to be \(x.\) Given that \(g = 10\,ms^{-2},\) the value of \(x\) will be close to ................ \(\mathrm{cm}\)

A block moving horizontally on a smooth surface with a speed of \(40\, {ms}^{-1}\) splits into two equal parts. If one of the parts moves at \(60\, {ms}^{-1}\) in the same direction, then the fractional change in the kinetic energy will be \(x: 4\) where \(x=..... .\)

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division \(=0.05 mm\), then the least count of the vernier callipers is _________ mm.

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : Body \('P'\) having mass \(M\) moving with speed \('u'\) has head-on collision elastically with another body \('Q'\) having mass \('m'\) initially at rest. If \(m< < M,\) body \('Q'\) will have a maximum speed equal to \('2u'\) after collision. Reason \(R\) : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:

In the following circuit, the magnitude of current \(I _{ l }\), is \(............A\).

A capacitor of capacitance \(\mathrm{C}\) and potential \(\mathrm{V}\) has energy \(E\). It is connected to another capacitor of capacitance \(2 \mathrm{C}\) and potential \(2 \mathrm{~V}\). Then the loss of energy is \(\frac{x}{3} E\), where \(\mathrm{x}\) is _______.

Given below are two statements: statement\(-I\) : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor. Statement\(-II\) : In \(ac\) circuit, the average power delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below