Find the resistance of a hollow cylindrical Conductor with the inner and outer radii of length 1.0 mm and 2.0 mm respectively. The resistivity of the material is 2.0 x 10^-8 \(\Omega\) m. The length of the conductor is 10 m.

1.  2.1 x 10^-3 \(\Omega\)

2.  1.3 x 10^-4 \(\Omega\)

3.  3.2 x 10^-4 \(\Omega\)

4.  4.6 x 10^-2 \(\Omega\)

A uniform ring of mass \(m\) and radius a is placed directly above a uniform sphere of mass m and of equal to radius. The centre of the ring is at a distance \(\sqrt3a\) from the centre of the sphere. The gravitational force (F) exerted by the sphere on the ring is:
1. \(\frac{3G~Mm}{8a^2}\)
2. \(\frac{2G~Mm}{3a^2}\)
3. \(\frac{7G~Mm}{\sqrt2a^2}\)
4. \(\frac{3G~Mm}{a^2}\)

A projectile is fired with a velocity \(u\) at angle \(\theta\) with the ground surface. During the motion at any time, it is making an angle \(\alpha\) with the ground surface. The speed of the particle at this time will be:
1. \(u\cos\theta~\sec\alpha\)
2. \(u\cos\theta.\tan\alpha\)
3. \(u^2\cos^2\theta.\sin\alpha\)
4. \(u\sin\theta.\sin\alpha\)

A horizontal tube of length \(l\) dosed at both ends contains an ideal gas of molecular weight \(M.\) The tube is rotated at a constant angular velocity \(\omega\) about a vertical axis passing through an end. Assuming the temperature to be uniform and constant. If \(P_1\) and \(P_2\) denote the pressure at the free and the fixed end respectively, then choose the correct relation.
1. \(\frac{P_2}{P_1}=e^{\frac{M\omega^2l^2}{2RT}}\)
2. \(\frac{P_1}{P_2}=e^{\frac{M\omega^2}{RT}}\)
3. \(\frac{P_1}{P_2}=e^{\frac{\omega lM}{3RT}}\)
4. \(\frac{P_2}{P_1}=e^{\frac{M^2\omega^2l^2}{3RT}}\)

The parts of two concentric circular arcs joined by two radial lines and carries current \(i.\) The arcs subtend an angle \(\theta\) at the centre of the circle the magnetic field at the centre \(O,\) is:
1. \(\frac{\mu_{_0}i(b-a)\theta}{4\pi ab}\)
2. \(\frac{\mu_{_0}i(b-a)}{4\pi ab}\)
3. \(\frac{\mu_{_0}i(b-a)\theta}{\pi ab}\)
4. \(\frac{\mu_{_0}i(a-b)}{2\pi ab}\)