A body of mass \(8\,kg\) and another of mass \(2\, kg\) are moving with equal kinetic energy. The ratio of their respective momenta will be.

A sinusoidal voltage \(V(t) = 100\,sin\,(500t)\) is applied across a pure inductance of \(L = 0.02\,H.\) The current through the coil is

A projectile is thrown upward at an angle \( 60^{\circ} \) with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is \( 45^{\circ} \) with the horizontal. The initial speed of the projectile is __________ in m/s.

A block of ice of mass \(120\,g\) at temperature \(0^{\circ} C\) is put in \(300\,gm\) of water at \(25^{\circ} C\). The \(xg\) of ice melts as the temperature of the water reaches \(0^{\circ} C\). The value of \(x\) is [Use: Specific heat capacity of water \(=4200\) \(J\,kg ^{-1} K ^{-1}\), Latent heat of ice \(\left.=3.5 \times 10^{5} J\,kg ^{-1}\right]\)

The photodiode is used to detect the optiocal signals. These diodes are preferably operated in reverse biased mode because.

Match List\(-I\) with List\(-II\)

List\(-I\)	List\(-II\)
\((a)\) \(h\) (Planck's constant)	\((i)\) \(\left[ M L T ^{-1}\right]\)
\((b)\) \(E\) (kinetic energy)	\((ii)\) \(\left[ M L ^{2} T ^{-1}\right]\)
\((c)\) \(V\) (electric potential)	\((iii)\) \(\left[ M L ^{2} T ^{-2}\right]\)
\((d)\) \(P\) (linear momentum)	\(( iv )\left[ M L ^{2} I ^{-1} T ^{-3}\right]\)

Choose the correct answer from the options given below

The minimum frequency of photon required to break a particle of mass 15.348 amu into 4\( \alpha \) particles is __________ kHz.
[mass of He nucleus = 4.002 amu,
\(1 amu =1.66 \times 10^{-27} kg, h =6.6 \times 10^{-34} J . s\) and \(c =\) \(\left.3 \times 10^8 m / s \right]\)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R / \sqrt{R^2+\omega^2 L^2}\right)\), where \(\omega\) is frequency of the supply across resistor \(R\) and inductor L . If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below :

In a fluorescent lamp choke (a small transformer) \(100 \;\mathrm{V}\) of reverse voltage is produced when the choke current changes uniformly from \(0.25 \;\mathrm{A}\) to \(0\;\mathrm{A}\) in a duration of \(0.025 \;\mathrm{ms} .\) The self-inductance of the choke (in \(\mathrm{mH})\) is estimated to be

A positive charge \('q'\) of mass \('m'\) is moving along the \(+ x\) axis. We wish to apply a uniform magnetic field \(B\) for time \(\Delta t\) so that the charge reverses its direction crossing the \(y\) axis at a distance \(d.\) Then