A highly rigid cubical block $A$ of small mass $M$ and side $L$ is fixed rigidly onto another cubical block $B$ of the same dimensions and of low modulus of rigidity $\eta $ such that the lower face of $A$ completely covers the upper face of $B$. The lower face of $B$is rigidly held on a horizontal surface. A small force $F$ is applied perpendicular to one of the side faces of $A$. After the force is withdrawn block $A$ executes small oscillations. The time period of which is given by
$2\pi \sqrt {\frac{{M\eta }}{L}} $
$2\pi \sqrt {\frac{L}{{M\eta }}} $
$2\pi \sqrt {\frac{{ML}}{\eta }} $
$2\pi \sqrt {\frac{M}{{\eta L}}} $
Planck's constant $(h),$ speed of light in vacuum $(c)$ and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length $?$
If force $F$ , velocity $V$ and time $T$ are taken as fundamental units then dimension of force in the pressure is
The potential energy $u$ of a particle varies with distance $x$ from a fixed origin as $u=\frac{A \sqrt{x}}{x+B}$, where $A$ and $B$ are constants. The dimensions of $A$ and $B$ are respectively
Even if a physical quantity depends upon three quantities, out of which two are dimensionally same, then the formula cannot be derived by the method of dimensions. This statement