$A$ hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in the figure. Let $V_A, V_B$,and $V_C$ be the potentials at points $A, B$,and $C$ respectively. Then:

$A$ simple harmonic oscillator consists of a particle of mass $m$ and an ideal spring with spring constant $k$. The particle oscillates with a time period $T$. The spring is cut into two equal parts. If one part oscillates with the same particle,the time period will be

Two soap bubbles of radii $r_1 = 4 \, cm$ and $r_2 = 5 \, cm$ are touching each other over a common surface $S_1S_2$ (as shown in the figure). The radius of curvature of this common surface will be ....... $cm$.

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

In a mass spectrometer used for measuring the masses of ions,the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant,the ratio $\left( \frac{\text{charge on the ion}}{\text{mass of the ion}} \right)$ will be proportional to

For intensity $I$ of a light of wavelength $5000 \mathring{A}$,the photoelectron saturation current is $0.40 \mu A$ and the stopping potential is $1.36 V$. The work function of the metal is ............. $eV$.