The minimum force required to start pushing a body up a rough (having coefficient of friction $\mu$) inclined plane is $F_1$,while the minimum force needed to prevent it from sliding down is $F_2$. If the inclined plane makes an angle $\theta$ with the horizontal such that $\tan \theta = 2\mu$,then the ratio $F_1 / F_2$ is

$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $V$,it has the same (total) energy stored in it as the first combination has. The value of $C_2$,in terms of $C_1$,is then

The calculated magnetic moment (in Bohr magnetons) of $Cu^{2+}$ ion is

In a series of $2n$ observations,half of them are equal to $a$ and the remaining half are equal to $-a$. If the standard deviation of the observations is $2$,then $|a|$ is equal to:

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ (where $r > a$) is ($\varepsilon_0$ is the permittivity of free space):

Choose the correct statement$(s)$:
$(A)$ The position of the centre of mass of a system is dependent on the choice of the coordinate system.
$(B)$ Newton's second law of motion is applicable to the centre of mass of the system.
$(C)$ Internal forces cannot change the state of the centre of mass.
$(D)$ Internal forces can change the state of the centre of mass.