MCQ
Two small spheres with masses $M_1$ and $M_2$ hang on weightless, insulating threads with lengths $L_1$ and $L_2$. The two spheres carry a charge of $Q_1$ and $Q_2$ respectively. The spheres hang such that they are level with one another and the threads are inclined to the vertical at angles $\theta_1$ and $\theta_2$. Which of the following conditions is required if $\theta_1=\theta_2$.
  • $M_1=M_2$
  • B
    $\left|Q_1\right|=\left|Q_2\right|$
  • C
    $L _1= L _2$
  • D
    None of these

Answer

Correct option: A.
$M_1=M_2$
a. $M _1= M _2$
Explanation:
$\theta_1=\theta_2$, if their masses are the same because the force of repulsion due to charges is the same.
The force $Mg \sin \theta$ opposes the force of repulsion. Even if $Q _1$ and $Q _2$ are different, the force of repulsion is the same for both as they are mutual.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

An alpha particle moving with an initial velocity $(uj)$enters a region of uniform magnetic field $B=Bk.$ the de$-$Broglie wavelength of the alpha particle.
If the current 30 A flowing in the primary coil is made zero in 0.1 sec. The emf induced in the secondary coil is 1.5 volt. The mutual inductance between the coil is
A $dc$ source of $emf \,E_1 = 100\,V$ and internal resistance $r = 0.5\,\Omega ,$ a storage battery of emf $E_2 = 90\,V$ and an external resistance $R$ are connected as shown in figure. For what value of $R$ no current will pass through the battery ? ................ $\Omega$
A cable of resistance $10\,\Omega $ carries electric power from a generator producing $250\, kW$ at $10000\, volt$, the power lost in the cable during transmission is ............. $kW$
A long horizontal metallic rod with length along the east-west direction is falling under gravity. The potential difference between its two ends will
The age of universe is believed to be
In the following circuit the equivalent resistance between $A$ and $B$ is......$\Omega $
If a proton and electron have same de Broglie wavelength, then:
Six point charges, each of the same magnitude $q$, are arranged in different manners as shown in Column $II$. In each case, a point $\mathrm{M}$ and a line $\mathrm{PQ}$ passing through $\mathrm{M}$ are shown. Let $E$ be the electric field and $V$ be the electric potential at $\mathrm{M}$ (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line $PQ$. Let $B$ be the magnetic field at $\mathrm{M}$ and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.
Column $I$ Column $II$
$(A)$ $E=0$ $Image$ Charges are at the corners of a regular hexagon. $\mathrm{M}$ is at the centre of the hexagon. $\mathrm{PQ}$ is perpendicular to the plane of the hexagon.
$(B)$ $V \neq 0$ $Image$ Charges are on a line perpendicular to $\mathrm{PQ}$ at equal intervals. $\mathrm{M}$ is the mid-point between the two innermost charges.
$(C)$ $B=0$ $Image$ Charges are placed on two coplanar insulating rings at equal intervals. $\mathrm{M}$ is the common centre of the rings. $\mathrm{PQ}$ is perpendicular to the plane of the rings.
$(D)$ $\mu \neq 0$ $Image$ Charges are placed at the corners of a rectangle of sides $a$ and $2 a$ and at the mid points of the longer sides. $\mathrm{M}$ is at the centre of the rectangle. $\mathrm{PQ}$ is parallel to the longer sides.
  $Image$ Charges are placed on two coplanar, identical insulating rings at equal intervals. $\mathrm{M}$ is the mid-point between the centres of the rings. $\mathrm{PQ}$ is perpendicular to the line joining the centres and coplanar to the rings.

Calculate the limit of resolution of a telescope objective having a diameter of $200\, cm$, if it has to detect light of wavelength $500\, nm$ coming from a star