A spring is stretched by \(5~\text{cm}\) by a force \(10~\text{N}\). The time period of the oscillations when a mass of \(2~\text{kg}\) is suspended by it is:
1. \(3.14~\text{s}\)
2. \(0.628~\text{s}\)
3. \(0.0628~\text{s}\)
4. \(6.28~\text{s}\)

An infinitely long straight conductor carries a current of \(5~\text{A}\) as shown. An electron is moving with a speed of ${\mathrm{}}^{}$\(10^5~\text{m/s}\) parallel to the conductor. The perpendicular distance between the electron and the conductor is \(20~\text{cm}\) at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

     
1. \(4\pi\times 10^{-20}~\text{N}\)
2. \(8\times 10^{-20}~\text{N}\)
3. \(4\times 10^{-20}~\text{N}\)
4. \(8\pi\times 10^{-20}~\text{N}\)

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:

1. $\frac{2}{3}$

2. $\frac{2}{3\sqrt{2}}$

3. $1/2$

4. $\frac{1}{2\sqrt{2}}$

Match Column - I and Column - II and choose the correct match from the given choices.
 

If \(E\) and \(G\), respectively, denote energy and gravitational constant, then \(\frac{E}{G}\) has the dimensions of:
1. \([ML^0T^0]\)
2. \([M^2L^{-2}T^{-1}]\)
3. \([M^2L^{-1}T^{0}]\)
4. \([ML^{-1}T^{-1}]\)

From a circular ring of mass \({M}\) and radius \(R\), an arc corresponding to a \(90^\circ\)$$sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \(K\) times \(MR^2\). The value of \(K\) will be:
1. \(\frac{1}{4}\)
2. \(\frac{1}{8}\)
3. \(\frac{3}{4}\)
4. \(\frac{7}{8}\)

A uniform conducting wire of length \(12a\) and resistance '\(R\)' is wound up as a current carrying coil in the shape of,
(i) an equilateral triangle of side '\(a\)'
(ii) a square of side '\(a\)'
The magnetic dipole moments of the coil in each case respectively are:
1. \(3Ia^2~\text{and}~4Ia^2\)
2. \(4Ia^2~\text{and}~3Ia^2\)
3. \(\sqrt{3}Ia^2~\text{and}~3Ia^2\)
4. \(3Ia^2~\text{and}~Ia^2\)

Two conducting circular loops of radii \(R_1\)$\mathrm{and}$\(R_2\) are placed in the same plane with their centres coinciding. If \(R_1>>R_2\) the mutual inductance \(M\) between them will be directly proportional to:
1. \(\frac{R^2_1}{R_2}\)
2. \(\frac{R^2_2}{R_1}\)
3. \(\frac{R_1}{R_2}\)
4. \(\frac{R_2}{R_1}\)

A ball of mass \(0.15~\text{kg}\) is dropped from a height \(10~\text{m}\), strikes the ground, and rebounds to the same height. The magnitude of impulse imparted to the ball is \((g=10 ~\text{m}/\text{s}^2)\) nearly:
1. \(2.1~\text{kg-m/s}\)
2. \(1.4~\text{kg-m/s}\)
3. \(0~\text{kg-m/s}\)
4. \(4.2~\text{kg-m/s}\)