41.

To reduce the range of voltmeter, its resistance needs to be reduced. A voltmeter has resistance Ro and ranges V. Which of the following resistances when connected in parallel will convert it into a voltmeter of range V/n?

• nR₀

• (n+1)R₀

• (n-1)R

• None of these

Two condensers, one of capacity C and the other of capacity C/2, are connected to a V- volt battery, as shown.

The work done in charging fully both the condensers is

• CV²

• $\frac{1}{4}{\mathrm{CV}}^2$

• $\frac{3}{4}{\mathrm{CV}}^2$

• $\frac{1}{2}{\mathrm{CV}}^2$

A capacitor of capacitance 5μF is connected as shown in the figure. The internal resistance of the hell is 0.5 Ω. The amount of charge on the capacitor plates is

• 80μC

• 40 μC

• 20 μC

• 10μC

You are given resistance wire of length 50 cm and a battery of negligible resistance. In which of the following cases is the largest amount of heat generated?

• When the wire is connected to the battery directly

• When the wire is divided into two parts and both the parts are connected to the battery in parallel.

• When the wire is divided into four parts and all the four parts are connected to the battery in parallel.

• When only half of the wire is connected to the battery

When the radioactive isotope ${}_{88}\mathrm{R\alpha }^{226}$ decays in a series by the emission of three alpha (α) and a beta (β) particle, the isotope X which remains undecay is

• ${}_{83}\mathrm{X}^{214}$

• ${}_{83}\mathrm{X}^{218}$

• ${}_{83}\mathrm{X}^{220}$

• ${}_{83}\mathrm{X}^{223}$

N lamps each of resistance r, are fed by the machine of resistance R. If light emitted by any lamp is proportional to the square of the heat produced, prove that the most efficient way of arranging them is to place them in parallel arcs, each containing n lamps, where n is the integer nearest to.

• ${\left(\frac{\mathrm{r}}{\mathrm{NR}}\right)}^{3/2}$

• ${\left(\frac{\mathrm{NR}}{\mathrm{r}}\right)}^{1/2}$

• (NRr)^3/2

• (NRr)^1/2

Radioactive decay will occur as follows

$$\begin{gathered} {}_{86}{}^{220}\mathrm{Rn} \stackrel{ }{\to } {}_{84}{}^{216}\mathrm{PO} + {}_2{}^4\mathrm{He} \mathrm{Half} \mathrm{life} = 55\mathrm{s} \\ {}_{84}{}^{216}\mathrm{PO} \stackrel{ }{\to } {}_{82}{}^{212}\mathrm{Pb} + {}_2{}^4\mathrm{He} \mathrm{Half} \mathrm{life} = 0.66 \mathrm{s} \\ {}_{82}{}^{812}\mathrm{Pb} \stackrel{ }{\to } {}_{82}{}^{212}\mathrm{BL} + \mathrm{\lambda }°\mathrm{e} \mathrm{Half} \mathrm{life} = 10.6 \mathrm{h} \end{gathered}$$

If a certain mass of radon (Rn = 220) is allowed to decay in a certain container; then after 5 minutes the element with the greater mass will be

• radon

• polonium

• lead

• bismuth

White light is used to illuminate two slits in Young's double slit experiment. The separation between the slits is b and the screen is at a distance d (>>b) from the slits. At a point on the screen directly in front of one of the slits, which wavelengths are missing?

• $\frac{\mathrm{b}}{\mathrm{d}}, \frac{\mathrm{b}}{3\mathrm{d}}, \frac{\mathrm{b}}{5\mathrm{d}}$

• $\frac{{\mathrm{b}}^2}{2\mathrm{d}}, \frac{{\mathrm{b}}^2}{3\mathrm{d}}, \frac{{\mathrm{b}}^2}{6\mathrm{d}}$

• $\frac{{\mathrm{b}}^2}{\mathrm{d}}, \frac{{\mathrm{b}}^2}{3\mathrm{d}}, \frac{{\mathrm{b}}^2}{5\mathrm{d}}$

• $\frac{\mathrm{b}}{2\mathrm{d}}, \frac{\mathrm{b}}{3\mathrm{d}}, \frac{\mathrm{b}}{6\mathrm{d}}$

The wavelength λ of  a photon and the de-Broglie wavelength of an electron have the same value. Find the ratio of the energy of a photon to the kinetic energy of an electron in terms of mass m, the speed of light c and Planck constant.

• $\frac{\mathrm{\lambda mc}}{\mathrm{h}}$

• $\frac{\mathrm{hmc}}{\mathrm{\lambda }}$

• $\frac{2\mathrm{hmc}}{\mathrm{\lambda }}$

• $\frac{2\mathrm{\lambda mc}}{\mathrm{h}}$

A nucleus ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}$ has mass represented by m (A,Z). If m_p and m_n denote the mass of proton and neutron respectively and BE the binding energy (in MeV) then.

• $\mathrm{BE} = \left[\mathrm{m}\right(\mathrm{A},\mathrm{Z}) - {\mathrm{Zm}}_{\mathrm{p}} - (\mathrm{A}-\mathrm{Z}\left){\mathrm{m}}_{\mathrm{n}}\right]{\mathrm{C}}^2$

• $\mathrm{BE} = [{\mathrm{Zm}}_{\mathrm{p}} + (\mathrm{A} -\mathrm{Z}){\mathrm{m}}_{\mathrm{n}} - \mathrm{m}(\mathrm{A},\mathrm{Z}\left)\right]{\mathrm{c}}^2$

• $\mathrm{BE} = [{\mathrm{Zm}}_{\mathrm{p}} + {\mathrm{Am}}_{\mathrm{n}} - \mathrm{m} (\mathrm{A},\mathrm{Z}\left)\right]{\mathrm{c}}^2$

• $\mathrm{BE} = \mathrm{m} (\mathrm{A},\mathrm{Z}) - {\mathrm{Zm}}_{\mathrm{p}} - (\mathrm{A}-\mathrm{Z}) {\mathrm{m}}_{\mathrm{N}}$