Physics Test - 29

As the spheres are uniform, the mass is equally distributed about $Q$ along the $x$-axis, the center of mass is $Q$, the distance of the center of mass is $PQ$.

$CM$ can be calculated as:

The first sphere is centered at the origin $\left(x=0\right)$, the second sphere is centered at $x=PQ$, the third sphere is centered at $x=PR$.

$PR=2PQ$

$x_{cm}=\frac{\left(m\times 0\right)+\left(m\times PQ\right)+\left(m\times 2PQ\right)}{3m}$

$=\frac{3m\times PQ}{3m}$

$=PQ$

Given: $T_1=300K,T_2=250K,Q_1=?,Q_2=700cals$

As we have,$\frac{Q_1}{Q_2}=\frac{T_1}{T_2}\Rightarrow \frac{Q_1}{Q_2}-1=\frac{T_1}{T_2}-1$

$\Rightarrow \frac{Q_1-Q_2}{Q_2}=\frac{T_1-T_2}{T_2}$

$\Rightarrow \frac{Q_1-Q_2}{750}=\frac{300-250}{250}=\frac{50}{250}$

$Q_1=\frac{50}{250}\times 750+750=900cal$

As the de-Broglie wavelength is given by

$\lambda =\frac{h}{p}\Rightarrow \frac{h}{\sqrt{2mE}}$,$E$is the kinetic energy

$E=\frac{h^2}{2m{\lambda }^2}$

$E=\frac{{\left(6.6\times {10}^{-34}\right)}^2}{2\times 9.1\times {10}^{-31}\times {\left(10\times {10}^{-12}\right)}^2}=2.39\times {10}^{-15}J$

or$E=14958.7eV\approx 15keV$

In the equilateral triangle$ABC$,

$AB=BC=AC=10cm$

Point$C$is on the equator of magnet$N-S$.

Induction/Intensity at,

$C=\frac{M}{{\left(AC\right)}^3}\times \frac{{\mu }_0}{4\mathrm{\pi }}$

Induction/intensity,$=\frac{1}{{\left(0.1\right)}^3}\times {10}^{-7}T$

Induction/intensity at$C={10}^3\times {10}^{-7}={10}^{-4}T$

$\therefore$Magnetic induction at$C={10}^{-4}T$

Some materials when placed in an external magnetic field, acquire a very low magnetism in a direction opposite to the field. These materials when brought near the end of a strong magnet, get repelled. These materials are diamagnetic and this property of materials is called diamagnetism. This property is generally found in materials in which there is an even number of electrons in their atoms (or molecules) and pairs are formed with two electrons. In each pair, the spin of one electron is in a direction opposite to the spin of another electron. Hence, the electrons of each pair completely cancel the magnetic moment of each other. Thus, the net magnetic moment of each atom of such material is zero.

From Einstein's photoelectric equation

$hv=h{v}_0+e{V}_0$

$=6.2+5=11.2eV$

$\therefore \frac{hc}{\lambda }=11.2eV$

or$\lambda =\frac{hc}{11.2eV}$

$=\frac{6.6\times {10}^{-34}\times 3.0\times {10}^8}{11.2\times 1.6\times {10}^{-19}}$

$=1.1049\times {10}^{-7}$

$=1104.9\AA$

This incident radiation lies in ultra violet region.

For a pendulum,$T=2\mathrm{\pi }\sqrt{\left(\raisebox{1ex}{$\mathrm{l}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{g}$}\right.\right)}$where$l$is measured up to the center of gravity. The center of gravity of the system is at the center of the sphere when the hole is plugged. When unplugged, water drains out. The center of gravity goes on descending. When the bob becomes empty, the center of gravity is restored to the center.

Therefore, the Length of the pendulum first increases, then decreases to the original value.

An electric motor is a device that uses an electric current to turn an axle. An electric motor transforms electrical energy into mechanical energy.

Given,

The magnetic moment of a bar magnet,$M=2.0J{T}^{-1}$

Uniform magnetic field,$B=0.25T$

The potential energy of the dipole$=MB\left(\cos {\theta }_1-\cos {\theta }_2\right)$

$=MB\left(\cos 0-\cos 180\right)$

$=2MB$

$=2\times 2.0\times 0.25$

$=1.0J$